This file contains numerical data from proofs mentioned in paper. Explanation: alpha = 4/nu - parameter alpha was used in JKT to parametrize KS equation starting point - x_0 (section 4) fixed point - x_* (section 4) - a center of our estimate for fixed point difference fixed - starting : x^* - x_0 coordinate change - T (section 4) here the coordinate change is given by y=m*(x - shift) mInv=m^{-1} Log norm - l (section) diff. estm. - the error estimates for difference between x^* (a true fixed point) and x_* in various norms ------------------------------ Unimodal fixed point: nu=0.75+[-0.01,0.01] alpha=[5.26316,5.40541] dimensions m= 3 M=10 delta=0.03125 number of iterates=4 starting point : 0.712361 -0.123239 0.0101786 fixed point : 0.71169 -0.123058 0.01011 difference fixed - starting : -0.000670889 0.000180807 -6.86782e-05 Isolating neighborhood (the set N):[-3.176878e-04,2.272739e-04] [-3.618637e-03,3.756375e-03] [-2.566221e-02,2.711549e-02] W=7.116901e-01+[-2.550124e-02,2.550124e-02] -1.230583e-01+[-1.252828e-02,1.252828e-02] 1.010996e-02+[-1.734936e-03,1.734936e-03] ------------------------------------- Self-consistent bounds k=1 b=7.116901e-01+[-2.550124e-02,2.550124e-02] k=2 b=-1.230583e-01+[-1.252828e-02,1.252828e-02] k=3 b=1.010996e-02+[-1.734936e-03,1.734936e-03] k=4 b=-6.776467e-04+[-1.481847e-04,1.481847e-04] k=5 b=3.959939e-05+[-1.100209e-05,1.100209e-05] k=6 b=-2.141130e-06+[-7.109068e-07,7.109068e-07] k=7 b=1.097242e-07+[-4.215413e-08,4.215413e-08] k=8 b=-5.411803e-09+[-2.358934e-09,2.358934e-09] k=9 b=2.605064e-10+[-2.100326e-10,2.100326e-10] k=10 b=-1.224540e-11+[-3.577344e-10,3.577344e-10] Tail : 4.176065e+03/k^10 ------------------------------------- Galerkin errors (epsilons) k=1 -1.427326e-05+[-5.374380e-06,5.374380e-06] k=2 3.426702e-04+[-1.076234e-04,1.076234e-04] k=3 -2.946523e-03+[-7.476203e-04,7.476203e-04] ------------------------------------- Coordinate change: shift 7.123609e-01 -1.232391e-01 1.017863e-02 m - transition from old to new coordinates 3 -0.0090621 0.09949 1.0087 -0.39312 -1.1041 -0.069407 -1.1408 -0.21674 -0.0066056 mInv - transition from new to old coordinates 3 0.0065846 0.18519 -0.94042 -0.065071 -0.97779 0.33745 0.99786 0.098106 -0.041732 Log norm =-5.71648e-02 for coord=3 l_i :-4.47668e+01 -6.06201e+00 -5.71648e-02 -1.60602e+02 -4.25808e+02 -9.14725e+02 -1.72695e+03 -2.97966e+03 -4.80787e+03 -7.36458e+03 -1.08208e+04 diff. estm L2=1.03378e-01 H1=1.31273e-01 C0=8.31295e-02 C1=1.21162e-01 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-1.60876e-02,1.15057e-02] +[-5.22831e+01,-5.06504e+01]x_{1} \\ x'_{2}&=&[-2.74080e-02,2.84486e-02] +[-7.93269e+00,-7.57472e+00]x_{2} \\ x'_{3}&=&[-1.29174e-02,1.36473e-02] +[-5.48683e-01,-5.03375e-01]x_{3} \\ \end{eqnarray*} ******************************************************** Unimodal fixed point: nu=0.5+[-0.0001,0.0001] alpha=[7.9984,8.0016] dimensions m= 4 M=10 delta=0.00125 number of iterates=5 starting point : 0.726148 -0.239112 0.0325565 -0.00373058 fixed point : 0.726148 -0.239116 0.032543 -0.00371052 difference fixed - starting : 9.10442e-07 -3.2753e-06 -1.34837e-05 2.00619e-05 Isolating neighborhood (the set N):[1.798670e-05,2.048202e-05] [2.216866e-06,2.454038e-05] [-3.105922e-04,2.951626e-04] [-4.779383e-04,4.838703e-04] W=7.261485e-01+[-4.986745e-04,4.986745e-04] -2.391156e-01+[-5.772959e-04,5.772959e-04] 3.254305e-02+[-1.180619e-04,1.180619e-04] -3.710523e-03+[-1.893987e-05,1.893987e-05] ------------------------------------- Self-consistent bounds k=1 b=7.261485e-01+[-4.986745e-04,4.986745e-04] k=2 b=-2.391156e-01+[-5.772959e-04,5.772959e-04] k=3 b=3.254305e-02+[-1.180619e-04,1.180619e-04] k=4 b=-3.710523e-03+[-1.893987e-05,1.893987e-05] k=5 b=3.635287e-04+[-2.264285e-06,2.264285e-06] k=6 b=-3.291505e-05+[-2.493123e-07,2.493123e-07] k=7 b=2.813500e-06+[-2.503881e-08,2.503881e-08] k=8 b=-2.307650e-07+[-2.740674e-09,2.740674e-09] k=9 b=1.833751e-08+[-2.155525e-09,2.155525e-09] k=10 b=-1.421827e-09+[-4.605634e-09,4.605634e-09] Tail : 3.492134e+04/k^10 ------------------------------------- Galerkin errors (epsilons) k=1 -2.721967e-06+[-3.091152e-08,3.091152e-08] k=2 4.781506e-05+[-4.726829e-07,4.726829e-07] k=3 -5.280501e-04+[-4.580623e-06,4.580623e-06] k=4 2.175520e-03+[-1.524218e-05,1.524218e-05] ------------------------------------- Coordinate change: shift 7.261475e-01 -2.391122e-01 3.255653e-02 -3.730584e-03 m - transition from old to new coordinates 4 0.0010463 -0.014913 0.073418 1.0056 0.031612 -0.16238 -1.0307 -0.05381 1.6941 2.0253 0.18038 -0.0095544 -2.3266 -1.193 -0.07858 0.0058487 mInv - transition from new to old coordinates 4 -0.00095424 -0.020636 -0.44653 -0.75524 0.010299 0.10591 0.8811 0.64303 -0.053781 -0.99141 -0.1538 -0.12549 0.9985 0.073973 0.024759 0.019483 Log norm =-9.52032e-01 for coord=4 l_i :-1.03428e+02 -2.91278e+01 -2.41650e+00 -9.52032e-01 -2.65598e+02 -5.87433e+02 -1.12334e+03 -1.95189e+03 -3.16339e+03 -4.85987e+03 -7.15536e+03 diff. estm L2=3.05025e-03 H1=8.05540e-03 C0=3.31328e-03 C1=8.60991e-03 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[2.00900e-03,2.28665e-03] +[-1.11693e+02,-1.11642e+02]x_{1} \\ x'_{2}&=&[6.94735e-05,7.68649e-04] +[-3.13386e+01,-3.13218e+01]x_{2} \\ x'_{3}&=&[-9.75044e-04,9.26606e-04] +[-3.14563e+00,-3.13931e+00]x_{3} \\ x'_{4}&=&[-6.45842e-04,6.53858e-04] +[-1.35428e+00,-1.35131e+00]x_{4} \\ \end{eqnarray*} ****************************** Unimodal fixed point: nu= 0.3+[-0.0001,0.0001] alpha=[13.3289,13.3378] dimensions m= 4 M=10 delta=0.00625 number of iterates=5 starting point : 0.413563 -0.311886 0.0491108 -0.00907195 fixed point : 0.413556 -0.311869 0.0489728 -0.00899392 difference fixed - starting : -6.88136e-06 1.73142e-05 -0.000137983 7.80353e-05 Isolating neighborhood (the set N):[-7.395969e-05,-6.103356e-05] [9.655713e-05,1.752072e-04] [-1.457099e-03,1.457099e-03] [-1.457073e-03,1.457073e-03] W=4.135558e-01+[-1.324880e-03,1.324880e-03] -3.118688e-01+[-1.848878e-03,1.848878e-03] 4.897284e-02+[-4.664898e-04,4.664898e-04] -8.993919e-03+[-1.162346e-04,1.162346e-04] ------------------------------------- Self-consistent bounds k=1 b=4.135558e-01+[-1.324880e-03,1.324880e-03] k=2 b=-3.118688e-01+[-1.848878e-03,1.848878e-03] k=3 b=4.897284e-02+[-4.664898e-04,4.664898e-04] k=4 b=-8.993919e-03+[-1.162346e-04,1.162346e-04] k=5 b=1.164615e-03+[-1.876201e-05,1.876201e-05] k=6 b=-1.523120e-04+[-2.955521e-06,2.955521e-06] k=7 b=1.805661e-05+[-4.107461e-07,4.107461e-07] k=8 b=-2.092956e-06+[-5.726399e-08,5.726399e-08] k=9 b=2.329518e-07+[-1.874951e-08,1.874951e-08] k=10 b=-2.539993e-08+[-1.505708e-08,1.505708e-08] Tail : 9.590259e+04/k^10 ------------------------------------- Galerkin errors (epsilons) k=1 -2.131372e-05+[-6.210936e-07,6.210936e-07] k=2 2.337393e-04+[-6.028945e-06,6.028945e-06] k=3 -2.225202e-03+[-4.935733e-05,4.935733e-05] k=4 4.240546e-03+[-8.427882e-05,8.427882e-05] ------------------------------------- Coordinate change: shift 4.135626e-01 -3.118860e-01 4.911082e-02 -9.071953e-03 m - transition from old to new coordinates 4 -0.003336 0.038983 -0.075045 -1.0066 0.10609 -0.17888 -1.0417 -0.051591 -1.1351 0.17165 0.076683 -0.0025931 -0.87937 -1.3094 -0.10849 0.021158 mInv - transition from new to old coordinates 4 0.0025296 -0.049386 -0.80873 -0.099191 -0.022264 0.11636 0.55864 -0.70701 0.053524 -0.98888 -0.18016 0.11306 -0.99832 0.078394 0.037747 -0.035481 Log norm =-3.74445e-01 for coord=3 l_i :-5.39650e+01 -1.23476e+01 -3.74445e-01 -3.74445e-01 -1.44891e+02 -3.33074e+02 -6.49069e+02 -1.13954e+03 -1.85891e+03 -2.86846e+03 -4.23660e+03 diff. estm L2=9.43523e-03 H1=2.64081e-02 C0=1.07338e-02 C1=2.95443e-02 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-4.47756e-03,-3.69816e-03] +[-6.05921e+01,-6.05406e+01]x_{1} \\ x'_{2}&=&[1.46018e-03,2.64658e-03] +[-1.51224e+01,-1.51055e+01]x_{2} \\ x'_{3}&=&[-2.92333e-04,6.06482e-05] +[-5.90177e-01,-5.89458e-01]x_{3} +[9.84461e-01,9.85018e-01]x_{4} \\ x'_{4}&=&[-7.11972e-04,8.03073e-04] +[-9.86009e-01,-9.83169e-01]x_{3} +[-5.91541e-01,-5.88324e-01]x_{4} \\ \end{eqnarray*} ************************************* bimodal fixed point nu=0.125+[-0.0001,0.0001] alpha=[31.9744,32.0256] dimensions m= 8 M=16 delta=0.00625 number of iterates=8 starting point : 0 -1.4523 0 -0.478224 0 -0.0651131 0 -0.00746117 fixed point : 0 -1.45229 0 -0.478227 0 -0.0650857 0 -0.00742105 difference fixed - starting : 0 4.87524e-06 0 -2.82332e-06 0 2.73991e-05 0 4.01196e-05 Isolating neighborhood (the set N):[-1.678126e-08,1.678126e-08] [-1.844515e-08,1.844515e-08] [-1.313249e-07,1.313249e-07] [-1.313180e-07,1.313180e-07] [-4.877098e-05,-2.796939e-05] [-6.478277e-05,1.175539e-04] [-2.428283e-03,2.466889e-03] [-3.877621e-03,3.911817e-03] W=0.000000e+00+[-1.490130e-07,1.490130e-07] -1.452291e+00+[-4.036286e-03,4.036286e-03] 0.000000e+00+[-1.631313e-07,1.631313e-07] -4.782273e-01+[-4.670729e-03,4.670729e-03] 0.000000e+00+[-6.370586e-08,6.370586e-08] -6.508567e-02+[-9.561118e-04,9.561118e-04] 0.000000e+00+[-2.665106e-08,2.665106e-08] -7.421049e-03+[-1.536096e-04,1.536096e-04] ------------------------------------- Self-consistent bounds k=1 b=0.000000e+00+[-1.490130e-07,1.490130e-07] k=2 b=-1.452291e+00+[-4.036286e-03,4.036286e-03] k=3 b=0.000000e+00+[-1.631313e-07,1.631313e-07] k=4 b=-4.782273e-01+[-4.670729e-03,4.670729e-03] k=5 b=0.000000e+00+[-6.370586e-08,6.370586e-08] k=6 b=-6.508567e-02+[-9.561118e-04,9.561118e-04] k=7 b=0.000000e+00+[-2.665106e-08,2.665106e-08] k=8 b=-7.421049e-03+[-1.536096e-04,1.536096e-04] k=9 b=0.000000e+00+[-4.251434e-08,4.251434e-08] k=10 b=-7.271462e-04+[-1.834659e-05,1.834659e-05] k=11 b=0.000000e+00+[-1.435797e-07,1.435797e-07] k=12 b=-6.584388e-05+[-2.086209e-06,2.086209e-06] k=13 b=0.000000e+00+[-5.617732e-07,5.617732e-07] k=14 b=-5.629201e-06+[-4.840837e-07,4.840837e-07] k=15 b=0.000000e+00+[-1.151413e-06,1.151413e-06] k=16 b=-4.623471e-07+[-6.198564e-07,6.198564e-07] Tail : 9.753372e+05/k^8 ------------------------------------- Galerkin errors (epsilons) k=1 0.000000e+00+[-9.322355e-08,9.322355e-08] k=2 2.178919e-05+[-1.122744e-06,1.122744e-06] k=3 0.000000e+00+[-1.512663e-07,1.512663e-07] k=4 3.826994e-04+[-1.543631e-05,1.543631e-05] k=5 0.000000e+00+[-5.437162e-07,5.437162e-07] k=6 4.225879e-03+[-1.486393e-04,1.486393e-04] k=7 0.000000e+00+[-4.062194e-06,4.062194e-06] k=8 1.740752e-02+[-4.959743e-04,4.959743e-04] ------------------------------------- Coordinate change: shift 0.000000e+00 -1.452295e+00 0.000000e+00 -4.782245e-01 0.000000e+00 -6.511307e-02 0.000000e+00 -7.461168e-03 m - transition from old to new coordinates 8 0.0010345 0 0.02115 0 0.10558 0 -1.0108 0 -0.052859 0 -0.30459 0 1.0851 0 -0.074734 0 -1.1493 0 0.70442 0 -0.082427 0 -0.0026703 0 0.54466 0 0.9402 0 -0.18437 0 -0.00048143 0 0 0.0010463 0 0.014913 0 0.073418 0 -1.0056 0 -0.031612 0 -0.16238 0 1.0307 0 -0.053807 0 1.6941 0 -2.0252 0 0.18038 0 0.0095613 0 2.3265 0 -1.1929 0 0.078579 0 0.0058487 mInv - transition from new to old coordinates 8 -0.0011215 0.034854 -0.63935 0.49033 0 0 0 0 0 0 0 0 -0.00095733 0.020638 -0.44653 0.75525 -0.014117 0.1718 0.38572 0.83059 0 0 0 0 0 0 0 0 -0.010305 0.10592 -0.8811 0.64302 -0.072702 0.97881 0.078204 0.26014 0 0 0 0 0 0 0 0 -0.053779 0.99141 -0.1538 0.12548 -0.99725 0.10587 0.015585 0.045054 0 0 0 0 0 0 0 0 -0.9985 0.073973 -0.024759 0.019483 Log norm =-2.16881e+00 for coord=3 l_i :-2.19936e+02 -4.33406e+01 -2.16881e+00 -2.16881e+00 -4.13034e+02 -1.16093e+02 -9.18078e+00 -3.43617e+00 -6.58619e+02 -1.06204e+03 -1.61815e+03 -2.34933e+03 -3.29602e+03 -4.49291e+03 -5.98223e+03 -7.80705e+03 -1.00137e+04 diff. estm L2=2.23620e-02 H1=8.11868e-02 C0=2.24679e-02 C1=1.04634e-01 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-4.18366e-06,4.18366e-06] +[-2.49790e+02,-2.49305e+02]x_{1} \\ x'_{2}&=&[-9.58129e-07,9.58129e-07] +[-5.20822e+01,-5.19447e+01]x_{2} \\ x'_{3}&=&[-2.72248e-07,2.72248e-07] +[-3.11997e+00,-3.11460e+00]x_{3} +[4.62846e+00,4.64079e+00]x_{4} \\ x'_{4}&=&[-3.02200e-07,3.02200e-07] +[-4.63738e+00,-4.62963e+00]x_{3} +[-3.12601e+00,-3.10730e+00]x_{4} \\ x'_{5}&=&[-2.17645e-02,-1.25046e-02] +[-4.47082e+02,-4.46259e+02]x_{5} \\ x'_{6}&=&[-8.10992e-03,1.47161e-02] +[-1.25455e+02,-1.25186e+02]x_{6} \\ x'_{7}&=&[-3.04004e-02,3.08837e-02] +[-1.26205e+01,-1.25193e+01]x_{7} \\ x'_{8}&=&[-2.08903e-02,2.10746e-02] +[-5.43495e+00,-5.38741e+00]x_{8} \\ \end{eqnarray*} *********************************** bimodal fixed point nu= 0.1+[-0.0001,0.0001] alpha=[39.96,40.04] dimensions m= 8 M=16 delta=0.03125 number of iterates=8 starting point : 0 -1.25664 0 -0.559838 0 -0.0881988 0 -0.0123863 fixed point : 0 -1.25664 0 -0.559826 0 -0.088107 0 -0.0122934 difference fixed - starting : 0 2.9143e-06 0 1.18589e-05 0 9.17503e-05 0 9.28851e-05 Isolating neighborhood (the set N):[-7.955885e-08,7.955885e-08] [-1.160902e-07,1.160902e-07] [-8.260940e-07,8.260940e-07] [-8.262680e-07,8.262680e-07] [-1.097277e-04,-6.179407e-05] [-8.585085e-05,2.611832e-04] [-6.760040e-03,6.760040e-03] [-6.760040e-03,6.760040e-03] W=0.000000e+00+[-1.056292e-06,1.056292e-06] -1.256639e+00+[-4.973152e-03,4.973152e-03] 0.000000e+00+[-1.013224e-06,1.013224e-06] -5.598260e-01+[-7.657201e-03,7.657201e-03] 0.000000e+00+[-4.900971e-07,4.900971e-07] -8.810702e-02+[-1.767642e-03,1.767642e-03] 0.000000e+00+[-1.708395e-07,1.708395e-07] -1.229339e-02+[-3.523747e-04,3.523747e-04] ------------------------------------- Self-consistent bounds k=1 b=0.000000e+00+[-1.056292e-06,1.056292e-06] k=2 b=-1.256639e+00+[-4.973152e-03,4.973152e-03] k=3 b=0.000000e+00+[-1.013224e-06,1.013224e-06] k=4 b=-5.598260e-01+[-7.657201e-03,7.657201e-03] k=5 b=0.000000e+00+[-4.900971e-07,4.900971e-07] k=6 b=-8.810702e-02+[-1.767642e-03,1.767642e-03] k=7 b=0.000000e+00+[-1.708395e-07,1.708395e-07] k=8 b=-1.229339e-02+[-3.523747e-04,3.523747e-04] k=9 b=0.000000e+00+[-1.716160e-07,1.716160e-07] k=10 b=-1.435232e-03+[-5.005448e-05,5.005448e-05] k=11 b=0.000000e+00+[-4.424119e-07,4.424119e-07] k=12 b=-1.561101e-04+[-6.819494e-06,6.819494e-06] k=13 b=0.000000e+00+[-1.478743e-06,1.478743e-06] k=14 b=-1.599119e-05+[-1.533317e-06,1.533317e-06] k=15 b=0.000000e+00+[-2.319492e-06,2.319492e-06] k=16 b=-1.575121e-06+[-1.299660e-06,1.299660e-06] Tail : 1.713369e+06/k^8 ------------------------------------- Galerkin errors (epsilons) k=1 0.000000e+00+[-2.918889e-07,2.918889e-07] k=2 7.155368e-05+[-4.928244e-06,4.928244e-06] k=3 0.000000e+00+[-5.392129e-07,5.392129e-07] k=4 1.027898e-03+[-5.707205e-05,5.707205e-05] k=5 0.000000e+00+[-2.308272e-06,2.308272e-06] k=6 9.813948e-03+[-4.795414e-04,4.795414e-04] k=7 0.000000e+00+[-1.439109e-05,1.439109e-05] k=8 3.028311e-02+[-1.207742e-03,1.207742e-03] ------------------------------------- Coordinate change: shift 0.000000e+00 -1.256641e+00 0.000000e+00 -5.598378e-01 0.000000e+00 -8.819876e-02 0.000000e+00 -1.238627e-02 m - transition from old to new coordinates 8 0.0019799 0 0.034085 0 0.11907 0 -1.0139 0 -0.10598 0 -0.3775 0 1.1291 0 -0.083347 0 -0.52105 0 1.1119 0 -0.2046 0 -0.005576 0 0.92062 0 0.55178 0 -0.17357 0 0.00064309 0 0 0.0019347 0 0.02331 0 0.08173 0 -1.0071 0 -0.053944 0 -0.18596 0 1.0407 0 -0.058772 0 1.2782 0 0.21294 0 -0.066722 0 -0.0013831 0 2.2511 0 -2.1337 0 0.18658 0 0.017491 mInv - transition from new to old coordinates 8 -0.002049 0.05886 -0.40781 0.8622 0 0 0 0 0 0 0 0 -0.0016525 0.031627 0.67069 0.064158 -0.020808 0.20652 0.74815 0.44725 0 0 0 0 0 0 0 0 -0.015098 0.1205 0.72233 -0.40724 -0.08071 0.96916 0.21553 0.23373 0 0 0 0 0 0 0 0 -0.059149 0.98872 0.16561 -0.070289 -0.99652 0.12088 0.049667 0.044169 0 0 0 0 0 0 0 0 -0.99813 0.083091 0.031447 -0.015007 Log norm =-5.06106e-01 for coord=3 l_i :-1.60573e+02 -2.54552e+01 -5.06106e-01 -5.06106e-01 -3.11627e+02 -8.19265e+01 -4.52463e+00 -4.52463e+00 -4.95044e+02 -8.15841e+02 -1.25428e+03 -1.83434e+03 -2.58585e+03 -3.53685e+03 -4.72135e+03 -6.17375e+03 -7.93071e+03 diff. estm L2=3.35615e-02 H1=1.35073e-01 C0=3.50747e-02 C1=1.79070e-01 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-1.50563e-05,1.50563e-05] +[-1.89754e+02,-1.89268e+02]x_{1} \\ x'_{2}&=&[-4.18507e-06,4.18507e-06] +[-3.62005e+01,-3.60576e+01]x_{2} \\ x'_{3}&=&[-1.36315e-06,1.36315e-06] +[-2.11125e+00,-2.09208e+00]x_{3} +[3.71122e+00,3.72546e+00]x_{4} \\ x'_{4}&=&[-1.04385e-06,1.04385e-06] +[-3.72481e+00,-3.71335e+00]x_{3} +[-2.10546e+00,-2.09622e+00]x_{4} \\ x'_{5}&=&[-3.77309e-02,-2.12994e-02] +[-3.44684e+02,-3.43860e+02]x_{5} \\ x'_{6}&=&[-7.95694e-03,2.42073e-02] +[-9.29552e+01,-9.26833e+01]x_{6} \\ x'_{7}&=&[-6.94703e-03,6.32716e-03] +[-5.83043e+00,-5.81691e+00]x_{7} +[4.08360e+00,4.08953e+00]x_{8} \\ x'_{8}&=&[-3.73163e-02,3.82466e-02] +[-4.13267e+00,-4.04046e+00]x_{7} +[-5.84795e+00,-5.79938e+00]x_{8} \\ \end{eqnarray*} *************************************** bimodal fixed point nu= 0.08+[-1e-06,1e-06] alpha=[49.9994,50.0006] dimensions m= 12 M=24 delta=0.00025 number of iterates=7 starting point : 0 -0.947539 0 -0.61345 0 -0.0999563 0 -0.0170275 0 -0.00220541 0 -0.000277739 fixed point : 0 -0.947539 0 -0.61345 0 -0.0999563 0 -0.0170273 0 -0.00220484 0 -0.000277209 difference fixed - starting : 0 -1.63104e-11 0 2.36234e-09 0 5.30781e-09 0 1.47561e-07 0 5.65465e-07 0 5.29893e-07 Isolating neighborhood (the set N):[-2.882019e-12,2.882019e-12] [-1.166355e-12,1.166355e-12] [-7.733630e-13,7.733630e-13] [-2.348844e-12,2.348844e-12] [-1.020269e-10,1.020269e-10] [-1.020269e-10,1.020269e-10] [5.075935e-07,5.180636e-07] [-5.892987e-07,-5.082788e-07] [-2.045543e-07,4.552658e-07] [-2.529351e-06,2.548124e-06] [-9.203673e-05,9.203673e-05] [-9.203673e-05,9.203673e-05] W=0.000000e+00+[-1.108190e-10,1.108190e-10] -9.475394e-01+[-9.340218e-05,9.340218e-05] 0.000000e+00+[-5.940293e-11,5.940293e-11] -6.134504e-01+[-9.542215e-05,9.542215e-05] 0.000000e+00+[-3.484790e-11,3.484790e-11] -9.995629e-02+[-2.098320e-05,2.098320e-05] 0.000000e+00+[-6.743054e-12,6.743054e-12] -1.702735e-02+[-5.280374e-06,5.280374e-06] 0.000000e+00+[-2.571062e-12,2.571062e-12] -2.204843e-03+[-8.446390e-07,8.446390e-07] 0.000000e+00+[-3.124373e-12,3.124373e-12] -2.772088e-04+[-1.307359e-07,1.307359e-07] ------------------------------------- Self-consistent bounds k=1 b=0.000000e+00+[-1.108190e-10,1.108190e-10] k=2 b=-9.475394e-01+[-9.340218e-05,9.340218e-05] k=3 b=0.000000e+00+[-5.940293e-11,5.940293e-11] k=4 b=-6.134504e-01+[-9.542215e-05,9.542215e-05] k=5 b=0.000000e+00+[-3.484790e-11,3.484790e-11] k=6 b=-9.995629e-02+[-2.098320e-05,2.098320e-05] k=7 b=0.000000e+00+[-6.743054e-12,6.743054e-12] k=8 b=-1.702735e-02+[-5.280374e-06,5.280374e-06] k=9 b=0.000000e+00+[-2.571062e-12,2.571062e-12] k=10 b=-2.204843e-03+[-8.446390e-07,8.446390e-07] k=11 b=0.000000e+00+[-3.124373e-12,3.124373e-12] k=12 b=-2.772088e-04+[-1.307359e-07,1.307359e-07] k=13 b=0.000000e+00+[-1.017490e-11,1.017490e-11] k=14 b=-3.224537e-05+[-1.762234e-08,1.762234e-08] k=15 b=0.000000e+00+[-4.120550e-11,4.120550e-11] k=16 b=-3.629114e-06+[-2.298289e-09,2.298289e-09] k=17 b=0.000000e+00+[-1.896719e-10,1.896719e-10] k=18 b=-3.942781e-07+[-3.848485e-10,3.848485e-10] k=19 b=0.000000e+00+[-7.552549e-10,7.552549e-10] k=20 b=-4.183680e-08+[-4.681436e-10,4.681436e-10] k=21 b=0.000000e+00+[-3.312567e-09,3.312567e-09] k=22 b=-4.348089e-09+[-1.948595e-09,1.948595e-09] k=23 b=0.000000e+00+[-4.735147e-09,4.735147e-09] k=24 b=-4.446007e-10+[-2.831228e-09,2.831228e-09] Tail : 1.704841e+08/k^10 ------------------------------------- Galerkin errors (epsilons) k=1 0.000000e+00+[-1.734248e-11,1.734248e-11] k=2 3.622868e-08+[-6.076426e-11,6.076426e-11] k=3 0.000000e+00+[-2.514716e-11,2.514716e-11] k=4 5.769188e-07+[-5.611902e-10,5.611902e-10] k=5 0.000000e+00+[-2.514254e-11,2.514254e-11] k=6 6.685985e-06+[-5.762368e-09,5.762368e-09] k=7 0.000000e+00+[-6.026887e-11,6.026887e-11] k=8 5.257284e-05+[-3.998506e-08,3.998506e-08] k=9 0.000000e+00+[-4.277392e-10,4.277392e-10] k=10 4.030099e-04+[-2.841728e-07,2.841728e-07] k=11 0.000000e+00+[-3.004307e-09,3.004307e-09] k=12 7.876840e-04+[-5.176148e-07,5.176148e-07] ------------------------------------- Coordinate change: shift 0.000000e+00 -9.475394e-01 0.000000e+00 -6.134504e-01 0.000000e+00 -9.995629e-02 0.000000e+00 -1.702749e-02 0.000000e+00 -2.205408e-03 0.000000e+00 -2.777387e-04 m - transition from old to new coordinates 12 -7.738e-06 0 -0.00016721 0 -0.0015908 0 -0.014274 0 -0.0348 0 1.0016 0 0.00015827 0 0.0024256 0 0.024625 0 0.056649 0 -1.0056 0 0.027546 0 -0.0034171 0 -0.052535 0 -0.11329 0 1.019 0 -0.043076 0 -0.0086931 0 0.22322 0 0.42498 0 -1.1733 0 0.081584 0 0.013935 0 0.00018501 0 0.99537 0 -0.21649 0 -0.045773 0 0.0068546 0 0.00065808 0 -6.134e-06 0 -0.43163 0 -2.4391 0 0.61736 0 0.022259 0 -0.0058853 0 -0.00043508 0 0 -1.0181e-05 0 -0.00015001 0 -0.0013027 0 -0.011371 0 -0.028183 0 1.0011 0 0.00017478 0 0.001962 0 0.018377 0 0.043337 0 -1.0035 0 0.022941 0 -0.0029535 0 -0.034668 0 -0.077387 0 1.0099 0 -0.034112 0 -0.0073255 0 0.090857 0 0.18659 0 -1.0442 0 0.056579 0 0.010556 0 0.00032527 0 0.51825 0 0.91985 0 -0.13622 0 -0.01243 0 0.00060501 0 9.549e-05 0 1.6264 0 -1.2182 0 0.074736 0 0.016939 0 7.9809e-05 0 -6.9723e-05 mInv - transition from new to old coordinates 12 1.0084e-05 -0.00017475 0.0031087 -0.092919 0.98071 -0.1033 0 0 0 0 0 0 0 0 0 0 0 0 1.1144e-05 -0.00017305 0.002445 -0.045116 0.58149 0.43209 0.00015441 -0.0019265 0.028855 -0.22788 -0.13873 -0.43801 0 0 0 0 0 0 0 0 0 0 0 0 0.00013408 -0.0015346 0.020711 -0.12197 0.78883 -0.24451 0.0012328 -0.015676 0.080888 -0.96124 0.13718 -0.18142 0 0 0 0 0 0 0 0 0 0 0 0 0.0010109 -0.012289 0.058387 -0.98796 0.194 -0.0065199 0.0098544 -0.044343 0.99445 -0.12027 0.011554 -0.043445 0 0 0 0 0 0 0 0 0 0 0 0 0.0081182 -0.034943 0.99701 -0.080787 0.043895 -0.0076597 0.027966 -0.99827 0.058518 -0.030997 0.0038436 -0.0079971 0 0 0 0 0 0 0 0 0 0 0 0 0.023223 -0.99891 0.044456 -0.021893 0.0071165 -0.00085647 0.99956 -0.035343 0.016339 -0.0043567 0.00050052 -0.0012591 0 0 0 0 0 0 0 0 0 0 0 0 0.9997 -0.028536 0.012656 -0.0028385 0.0010755 -0.00015185 Log norm =-8.68186e-01 for coord=5 l_i :-1.01202e+03 -4.29071e+02 -1.40031e+02 -2.31355e+01 -8.68186e-01 -8.68186e-01 -1.47339e+03 -6.83845e+02 -2.60610e+02 -6.65182e+01 -3.05513e+00 -3.05513e+00 -2.02431e+03 -2.77970e+03 -3.72258e+03 -4.87801e+03 -6.27810e+03 -7.95283e+03 -9.93690e+03 -1.22655e+04 -1.49763e+04 -1.81086e+04 -2.17037e+04 -2.58047e+04 -3.04569e+04 diff. estm L2=4.93310e-04 H1=2.27515e-03 C0=5.21669e-04 C1=2.94327e-03 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-3.02482e-09,3.02482e-09] +[-1.04958e+03,-1.04955e+03]x_{1} \\ x'_{2}&=&[-5.17328e-10,5.17328e-10] +[-4.43556e+02,-4.43543e+02]x_{2} \\ x'_{3}&=&[-1.10335e-10,1.10335e-10] +[-1.42674e+02,-1.42669e+02]x_{3} \\ x'_{4}&=&[-5.56847e-11,5.56847e-11] +[-2.37087e+01,-2.37073e+01]x_{4} \\ x'_{5}&=&[-2.46079e-11,2.46079e-11] +[-9.12441e-01,-9.12426e-01]x_{5} +[1.67556e+00,1.67559e+00]x_{6} \\ x'_{6}&=&[-8.97545e-11,8.97545e-11] +[-1.67565e+00,-1.67549e+00]x_{5} +[-9.12593e-01,-9.12274e-01]x_{6} \\ x'_{7}&=&[7.68626e-04,7.84458e-04] +[-1.51425e+03,-1.51421e+03]x_{7} \\ x'_{8}&=&[-4.12341e-04,-3.55660e-04] +[-6.99735e+02,-6.99715e+02]x_{8} \\ x'_{9}&=&[-5.38757e-05,1.19908e-04] +[-2.63389e+02,-2.63381e+02]x_{9} \\ x'_{10}&=&[-1.69596e-04,1.70854e-04] +[-6.70538e+01,-6.70511e+01]x_{10} \\ x'_{11}&=&[-1.71625e-04,1.70107e-04] +[-3.09888e+00,-3.09842e+00]x_{11} +[4.29590e+00,4.29603e+00]x_{12} \\ x'_{12}&=&[-2.26056e-04,2.27701e-04] +[-4.29625e+00,-4.29568e+00]x_{11} +[-3.09874e+00,-3.09856e+00]x_{12} \\ \end{eqnarray*} **************************************** bimodal fixed point nu= 0.08+[-1e-06,1e-06] alpha=[49.9994,50.0006] dimensions m= 12 M=24 delta=0.00025 number of iterates=7 starting point : 0 -0.947539 0 -0.61345 0 -0.0999563 0 -0.0170275 0 -0.00220541 0 -0.000277739 fixed point : 0 -0.947539 0 -0.61345 0 -0.0999563 0 -0.0170273 0 -0.00220484 0 -0.000277209 difference fixed - starting : 0 -1.63104e-11 0 2.36234e-09 0 5.30781e-09 0 1.47561e-07 0 5.65465e-07 0 5.29893e-07 Isolating neighborhood (the set N):[-2.882019e-12,2.882019e-12] [-1.166355e-12,1.166355e-12] [-7.733630e-13,7.733630e-13] [-2.348844e-12,2.348844e-12] [-1.020269e-10,1.020269e-10] [-1.020269e-10,1.020269e-10] [5.075935e-07,5.180636e-07] [-5.892987e-07,-5.082788e-07] [-2.045543e-07,4.552658e-07] [-2.529351e-06,2.548124e-06] [-9.203673e-05,9.203673e-05] [-9.203673e-05,9.203673e-05] W=0.000000e+00+[-1.108190e-10,1.108190e-10] -9.475394e-01+[-9.340218e-05,9.340218e-05] 0.000000e+00+[-5.940293e-11,5.940293e-11] -6.134504e-01+[-9.542215e-05,9.542215e-05] 0.000000e+00+[-3.484790e-11,3.484790e-11] -9.995629e-02+[-2.098320e-05,2.098320e-05] 0.000000e+00+[-6.743054e-12,6.743054e-12] -1.702735e-02+[-5.280374e-06,5.280374e-06] 0.000000e+00+[-2.571062e-12,2.571062e-12] -2.204843e-03+[-8.446390e-07,8.446390e-07] 0.000000e+00+[-3.124373e-12,3.124373e-12] -2.772088e-04+[-1.307359e-07,1.307359e-07] ------------------------------------- Self-consistent bounds k=1 b=0.000000e+00+[-1.108190e-10,1.108190e-10] k=2 b=-9.475394e-01+[-9.340218e-05,9.340218e-05] k=3 b=0.000000e+00+[-5.940293e-11,5.940293e-11] k=4 b=-6.134504e-01+[-9.542215e-05,9.542215e-05] k=5 b=0.000000e+00+[-3.484790e-11,3.484790e-11] k=6 b=-9.995629e-02+[-2.098320e-05,2.098320e-05] k=7 b=0.000000e+00+[-6.743054e-12,6.743054e-12] k=8 b=-1.702735e-02+[-5.280374e-06,5.280374e-06] k=9 b=0.000000e+00+[-2.571062e-12,2.571062e-12] k=10 b=-2.204843e-03+[-8.446390e-07,8.446390e-07] k=11 b=0.000000e+00+[-3.124373e-12,3.124373e-12] k=12 b=-2.772088e-04+[-1.307359e-07,1.307359e-07] k=13 b=0.000000e+00+[-1.017490e-11,1.017490e-11] k=14 b=-3.224537e-05+[-1.762234e-08,1.762234e-08] k=15 b=0.000000e+00+[-4.120550e-11,4.120550e-11] k=16 b=-3.629114e-06+[-2.298289e-09,2.298289e-09] k=17 b=0.000000e+00+[-1.896719e-10,1.896719e-10] k=18 b=-3.942781e-07+[-3.848485e-10,3.848485e-10] k=19 b=0.000000e+00+[-7.552549e-10,7.552549e-10] k=20 b=-4.183680e-08+[-4.681436e-10,4.681436e-10] k=21 b=0.000000e+00+[-3.312567e-09,3.312567e-09] k=22 b=-4.348089e-09+[-1.948595e-09,1.948595e-09] k=23 b=0.000000e+00+[-4.735147e-09,4.735147e-09] k=24 b=-4.446007e-10+[-2.831228e-09,2.831228e-09] Tail : 1.704841e+08/k^10 ------------------------------------- Galerkin errors (epsilons) k=1 0.000000e+00+[-1.734248e-11,1.734248e-11] k=2 3.622868e-08+[-6.076426e-11,6.076426e-11] k=3 0.000000e+00+[-2.514716e-11,2.514716e-11] k=4 5.769188e-07+[-5.611902e-10,5.611902e-10] k=5 0.000000e+00+[-2.514254e-11,2.514254e-11] k=6 6.685985e-06+[-5.762368e-09,5.762368e-09] k=7 0.000000e+00+[-6.026887e-11,6.026887e-11] k=8 5.257284e-05+[-3.998506e-08,3.998506e-08] k=9 0.000000e+00+[-4.277392e-10,4.277392e-10] k=10 4.030099e-04+[-2.841728e-07,2.841728e-07] k=11 0.000000e+00+[-3.004307e-09,3.004307e-09] k=12 7.876840e-04+[-5.176148e-07,5.176148e-07] ------------------------------------- Coordinate change: shift 0.000000e+00 -9.475394e-01 0.000000e+00 -6.134504e-01 0.000000e+00 -9.995629e-02 0.000000e+00 -1.702749e-02 0.000000e+00 -2.205408e-03 0.000000e+00 -2.777387e-04 m - transition from old to new coordinates 12 -7.738e-06 0 -0.00016721 0 -0.0015908 0 -0.014274 0 -0.0348 0 1.0016 0 0.00015827 0 0.0024256 0 0.024625 0 0.056649 0 -1.0056 0 0.027546 0 -0.0034171 0 -0.052535 0 -0.11329 0 1.019 0 -0.043076 0 -0.0086931 0 0.22322 0 0.42498 0 -1.1733 0 0.081584 0 0.013935 0 0.00018501 0 0.99537 0 -0.21649 0 -0.045773 0 0.0068546 0 0.00065808 0 -6.134e-06 0 -0.43163 0 -2.4391 0 0.61736 0 0.022259 0 -0.0058853 0 -0.00043508 0 0 -1.0181e-05 0 -0.00015001 0 -0.0013027 0 -0.011371 0 -0.028183 0 1.0011 0 0.00017478 0 0.001962 0 0.018377 0 0.043337 0 -1.0035 0 0.022941 0 -0.0029535 0 -0.034668 0 -0.077387 0 1.0099 0 -0.034112 0 -0.0073255 0 0.090857 0 0.18659 0 -1.0442 0 0.056579 0 0.010556 0 0.00032527 0 0.51825 0 0.91985 0 -0.13622 0 -0.01243 0 0.00060501 0 9.549e-05 0 1.6264 0 -1.2182 0 0.074736 0 0.016939 0 7.9809e-05 0 -6.9723e-05 mInv - transition from new to old coordinates 12 1.0084e-05 -0.00017475 0.0031087 -0.092919 0.98071 -0.1033 0 0 0 0 0 0 0 0 0 0 0 0 1.1144e-05 -0.00017305 0.002445 -0.045116 0.58149 0.43209 0.00015441 -0.0019265 0.028855 -0.22788 -0.13873 -0.43801 0 0 0 0 0 0 0 0 0 0 0 0 0.00013408 -0.0015346 0.020711 -0.12197 0.78883 -0.24451 0.0012328 -0.015676 0.080888 -0.96124 0.13718 -0.18142 0 0 0 0 0 0 0 0 0 0 0 0 0.0010109 -0.012289 0.058387 -0.98796 0.194 -0.0065199 0.0098544 -0.044343 0.99445 -0.12027 0.011554 -0.043445 0 0 0 0 0 0 0 0 0 0 0 0 0.0081182 -0.034943 0.99701 -0.080787 0.043895 -0.0076597 0.027966 -0.99827 0.058518 -0.030997 0.0038436 -0.0079971 0 0 0 0 0 0 0 0 0 0 0 0 0.023223 -0.99891 0.044456 -0.021893 0.0071165 -0.00085647 0.99956 -0.035343 0.016339 -0.0043567 0.00050052 -0.0012591 0 0 0 0 0 0 0 0 0 0 0 0 0.9997 -0.028536 0.012656 -0.0028385 0.0010755 -0.00015185 Log norm =-8.68186e-01 for coord=5 l_i :-1.01202e+03 -4.29071e+02 -1.40031e+02 -2.31355e+01 -8.68186e-01 -8.68186e-01 -1.47339e+03 -6.83845e+02 -2.60610e+02 -6.65182e+01 -3.05513e+00 -3.05513e+00 -2.02431e+03 -2.77970e+03 -3.72258e+03 -4.87801e+03 -6.27810e+03 -7.95283e+03 -9.93690e+03 -1.22655e+04 -1.49763e+04 -1.81086e+04 -2.17037e+04 -2.58047e+04 -3.04569e+04 diff. estm L2=4.93310e-04 H1=2.27515e-03 C0=5.21669e-04 C1=2.94327e-03 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-3.02482e-09,3.02482e-09] +[-1.04958e+03,-1.04955e+03]x_{1} \\ x'_{2}&=&[-5.17328e-10,5.17328e-10] +[-4.43556e+02,-4.43543e+02]x_{2} \\ x'_{3}&=&[-1.10335e-10,1.10335e-10] +[-1.42674e+02,-1.42669e+02]x_{3} \\ x'_{4}&=&[-5.56847e-11,5.56847e-11] +[-2.37087e+01,-2.37073e+01]x_{4} \\ x'_{5}&=&[-2.46079e-11,2.46079e-11] +[-9.12441e-01,-9.12426e-01]x_{5} +[1.67556e+00,1.67559e+00]x_{6} \\ x'_{6}&=&[-8.97545e-11,8.97545e-11] +[-1.67565e+00,-1.67549e+00]x_{5} +[-9.12593e-01,-9.12274e-01]x_{6} \\ x'_{7}&=&[7.68626e-04,7.84458e-04] +[-1.51425e+03,-1.51421e+03]x_{7} \\ x'_{8}&=&[-4.12341e-04,-3.55660e-04] +[-6.99735e+02,-6.99715e+02]x_{8} \\ x'_{9}&=&[-5.38757e-05,1.19908e-04] +[-2.63389e+02,-2.63381e+02]x_{9} \\ x'_{10}&=&[-1.69596e-04,1.70854e-04] +[-6.70538e+01,-6.70511e+01]x_{10} \\ x'_{11}&=&[-1.71625e-04,1.70107e-04] +[-3.09888e+00,-3.09842e+00]x_{11} +[4.29590e+00,4.29603e+00]x_{12} \\ x'_{12}&=&[-2.26056e-04,2.27701e-04] +[-4.29625e+00,-4.29568e+00]x_{11} +[-3.09874e+00,-3.09856e+00]x_{12} \\ \end{eqnarray*} ***************************** a stable fixed point close to R_3t_2 nu= 0.08+[-1e-06,1e-06] alpha=[49.9994,50.0006] dimensions m= 18 M=36 delta=0.00125 number of iterates=8 starting point : 0.0527449 0.144244 2.15945 -0.182292 -0.113855 -0.39381 0.0417122 0.0170906 0.0331428 -0.00491577 -0.00164365 -0.00222004 0.000434272 0.000122333 0.000126963 -3.22106e-05 -7.7832e-06 -6.54668e-06 fixed point : 0.0527449 0.144243 2.15945 -0.182292 -0.113854 -0.39381 0.0417121 0.0170906 0.0331428 -0.00491576 -0.00164364 -0.00222004 0.000434262 0.000122329 0.000126959 -3.21814e-05 -7.77663e-06 -6.54276e-06 difference fixed - starting : -6.82685e-08 -3.55167e-07 1.42545e-07 4.08787e-07 3.02418e-07 -6.57781e-08 -9.4891e-08 -4.7776e-08 1.04104e-08 1.27464e-08 5.619e-09 2.04016e-10 -1.04093e-08 -4.17278e-09 -4.2482e-09 2.92345e-08 6.57043e-09 3.91796e-09 Isolating neighborhood (the set N):[-4.063711e-09,-3.766208e-09] [-6.743506e-09,-6.298672e-09] [-2.967848e-08,-2.821101e-08] [1.853879e-09,6.703460e-09] [1.156145e-09,6.275530e-09] [8.622398e-10,1.676827e-08] [-4.266049e-08,3.961067e-08] [-3.159194e-08,3.451223e-08] [-9.153971e-08,9.368113e-08] [-6.384564e-07,6.439827e-07] [-3.651752e-07,3.772513e-07] [-9.324962e-07,9.332558e-07] [-1.032778e-05,1.029924e-05] [-3.546883e-05,3.545140e-05] [-7.029264e-05,7.053945e-05] [-1.836221e-04,1.836221e-04] [-1.836221e-04,1.836221e-04] [-6.775927e-04,6.764684e-04] W=5.274488e-02+[-1.602411e-04,1.602411e-04] 1.442435e-01+[-5.056466e-04,5.056466e-04] 2.159446e+00+[-3.287726e-04,3.287726e-04] -1.822917e-01+[-6.503868e-04,6.503868e-04] -1.138543e-01+[-4.218164e-04,4.218164e-04] -3.938097e-01+[-1.619996e-04,1.619996e-04] 4.171209e-02+[-1.511033e-04,1.511033e-04] 1.709057e-02+[-5.805989e-05,5.805989e-05] 3.314285e-02+[-2.674301e-05,2.674301e-05] -4.915757e-03+[-1.804354e-05,1.804354e-05] -1.643644e-03+[-5.014780e-06,5.014780e-06] -2.220037e-03+[-2.986030e-06,2.986030e-06] 4.342618e-04+[-1.582435e-06,1.582435e-06] 1.223293e-04+[-3.148142e-07,3.148142e-07] 1.269587e-04+[-2.620929e-07,2.620929e-07] -3.218136e-05+[-1.147979e-07,1.147979e-07] -7.776635e-06+[-1.521837e-08,1.521837e-08] -6.542764e-06+[-1.973409e-08,1.973409e-08] ------------------------------------- Self-consistent bounds k=1 b=5.274488e-02+[-1.602411e-04,1.602411e-04] k=2 b=1.442435e-01+[-5.056466e-04,5.056466e-04] k=3 b=2.159446e+00+[-3.287726e-04,3.287726e-04] k=4 b=-1.822917e-01+[-6.503868e-04,6.503868e-04] k=5 b=-1.138543e-01+[-4.218164e-04,4.218164e-04] k=6 b=-3.938097e-01+[-1.619996e-04,1.619996e-04] k=7 b=4.171209e-02+[-1.511033e-04,1.511033e-04] k=8 b=1.709057e-02+[-5.805989e-05,5.805989e-05] k=9 b=3.314285e-02+[-2.674301e-05,2.674301e-05] k=10 b=-4.915757e-03+[-1.804354e-05,1.804354e-05] k=11 b=-1.643644e-03+[-5.014780e-06,5.014780e-06] k=12 b=-2.220037e-03+[-2.986030e-06,2.986030e-06] k=13 b=4.342618e-04+[-1.582435e-06,1.582435e-06] k=14 b=1.223293e-04+[-3.148142e-07,3.148142e-07] k=15 b=1.269587e-04+[-2.620929e-07,2.620929e-07] k=16 b=-3.218136e-05+[-1.147979e-07,1.147979e-07] k=17 b=-7.776635e-06+[-1.521837e-08,1.521837e-08] k=18 b=-6.542764e-06+[-1.973409e-08,1.973409e-08] k=19 b=2.123606e-06+[-9.657812e-09,9.657812e-09] k=20 b=4.405102e-07+[-2.981862e-09,2.981862e-09] k=21 b=3.101847e-07+[-1.400213e-09,1.400213e-09] k=22 b=-1.288147e-07+[-6.172656e-10,6.172656e-10] k=23 b=-2.273434e-08+[-1.883876e-10,1.883876e-10] k=24 b=-1.365218e-08+[-8.896289e-11,8.896289e-11] k=25 b=7.324265e-09+[-3.929642e-11,3.929642e-11] k=26 b=1.079070e-09+[-1.345009e-11,1.345009e-11] k=27 b=5.575168e-10+[-7.946981e-12,7.946981e-12] k=28 b=-3.953614e-10+[-1.378850e-11,1.378850e-11] k=29 b=-4.705115e-11+[-1.277656e-11,1.277656e-11] k=30 b=-2.087564e-11+[-1.806566e-11,1.806566e-11] k=31 b=2.043797e-11+[-9.516519e-11,9.516519e-11] k=32 b=1.856152e-12+[-8.466500e-11,8.466500e-11] k=33 b=6.929226e-13+[-8.820848e-11,8.820848e-11] k=34 b=-1.018066e-12+[-4.018720e-10,4.018720e-10] k=35 b=-6.327620e-14+[-2.891249e-10,2.891249e-10] k=36 b=-1.843854e-14+[-2.018985e-10,2.018985e-10] Tail : 1.625163e+12/k^12 ------------------------------------- Galerkin errors (epsilons) k=1 -2.571822e-11+[-6.378209e-13,6.378209e-13] k=2 -7.520143e-11+[-1.159216e-12,1.159216e-12] k=3 -4.445137e-10+[-4.268603e-12,4.268603e-12] k=4 2.030516e-09+[-1.626535e-11,1.626535e-11] k=5 3.068522e-09+[-2.494159e-11,2.494159e-11] k=6 1.223896e-08+[-1.008031e-10,1.008031e-10] k=7 -6.301156e-08+[-4.227954e-10,4.227954e-10] k=8 -6.963235e-08+[-5.717604e-10,5.717604e-10] k=9 -2.144284e-07+[-1.754596e-09,1.754596e-09] k=10 1.359652e-06+[-8.105080e-09,8.105080e-09] k=11 1.091783e-06+[-9.100762e-09,9.100762e-09] k=12 2.570279e-06+[-2.066487e-08,2.066487e-08] k=13 -2.123609e-05+[-1.145516e-07,1.145516e-07] k=14 -1.134636e-05+[-9.441608e-08,9.441608e-08] k=15 -1.697054e-05+[-1.296654e-07,1.296654e-07] k=16 1.446394e-04+[-7.345077e-07,7.345077e-07] k=17 4.162429e-05+[-3.304126e-07,3.304126e-07] k=18 3.157820e-05+[-1.762918e-07,1.762918e-07] ------------------------------------- Coordinate change: shift 5.274494e-02 1.442438e-01 2.159446e+00 -1.822920e-01 -1.138546e-01 -3.938095e-01 4.171218e-02 1.709062e-02 3.314283e-02 -4.915770e-03 -1.643649e-03 -2.220036e-03 4.342721e-04 1.223334e-04 1.269629e-04 -3.221059e-05 -7.783205e-06 -6.546682e-06 m - transition from old to new coordinates 18 -7.3758e-09 2.165e-08 -1.4448e-07 -1.8447e-07 -8.2699e-07 5.101e-06 4.4185e-06 1.5174e-05 -0.00011599 -6.728e-05 -0.00018525 0.0019854 0.00065705 0.0012408 -0.018336 -0.0016888 -0.0011219 -1.0004 1.7948e-08 -1.3306e-07 -1.7846e-07 -8.4138e-07 5.398e-06 4.8164e-06 1.6852e-05 -0.00013051 -7.6594e-05 -0.00021178 0.0022757 0.00075748 0.0014223 -0.020936 -0.0019629 -0.0012737 -1.0005 -0.0015163 -7.1733e-08 -1.4253e-07 -8.2614e-07 5.5649e-06 5.1778e-06 1.864e-05 -0.00014712 -8.7383e-05 -0.00024387 0.0026323 0.00087598 0.0016483 -0.024138 -0.0022388 -0.001534 -1.0007 -0.001338 -0.0013794 -7.4184e-08 -6.9593e-07 5.5016e-06 5.4329e-06 2.0447e-05 -0.00016572 -0.0001001 -0.00028277 0.003072 0.0010219 0.0019223 -0.028046 -0.0025385 -0.0016842 -1.0014 -0.0010797 -0.0016877 -0.015201 -6.0088e-07 4.9577e-06 5.5163e-06 2.2038e-05 -0.00018577 -0.00011523 -0.00033084 0.0036286 0.0012142 0.0022788 -0.033105 -0.0030156 -0.0019691 -1.0018 -0.0017512 -0.0019214 -0.017146 0.00095501 3.1678e-06 4.684e-06 2.29e-05 -0.00020519 -0.00013241 -0.00038996 0.0043397 0.0014601 0.0027425 -0.039685 -0.0035756 -0.0023341 -1.0025 -0.0018238 -0.0022255 -0.019491 0.0010763 0.00046175 2.6656e-06 2.1067e-05 -0.00021997 -0.00015082 -0.00046217 0.0052603 0.0017878 0.003363 -0.048463 -0.0043313 -0.0027946 -1.0036 -0.0021508 -0.0025783 -0.022398 0.0012161 0.00051383 0.0012236 -2.2501e-05 0.00021835 0.00016898 0.00054968 -0.006466 -0.0022345 -0.00422 0.060564 0.0053629 0.0034179 1.0052 0.0025749 0.0030329 0.02597 -0.001389 -0.0005746 -0.0013345 9.414e-05 0.00015851 0.0001541 0.00064761 -0.0080457 -0.0028583 -0.005451 0.077946 0.0068239 0.0042846 1.008 0.0031277 0.0036248 0.030491 -0.0015975 -0.00064529 -0.0014499 9.787e-05 2.4824e-05 -0.00010516 -0.00068936 0.01012 0.003759 0.0073047 -0.10432 -0.0090051 -0.005544 -1.0129 -0.003894 -0.0044194 -0.036356 0.0018554 0.0007258 0.0015626 -9.8968e-05 -2.2842e-05 -2.2415e-05 -0.0011145 0.012474 0.005203 0.010439 -0.14759 -0.012542 -0.0075466 -1.0228 -0.0050363 -0.0055397 -0.044231 0.0021801 0.00081726 0.0016548 -9.4878e-05 -1.8337e-05 -1.1654e-05 -3.6983e-07 0.012602 0.0054669 0.016157 -0.22747 -0.018416 -0.011069 -1.0451 -0.0067307 -0.0072436 -0.055431 0.0026065 0.0009192 0.0016935 -8.08e-05 -9.2769e-06 6.9417e-06 -2.9272e-06 -1.2805e-06 0.0068658 0.026384 -0.42995 -0.031261 -0.016322 -1.1237 -0.0095417 -0.010003 -0.074363 0.003281 0.0010509 0.0016384 -4.8158e-05 8.1579e-06 4.0312e-05 -7.156e-06 -2.4281e-06 -3.0686e-06 0.81013 -5.269 -0.55355 -1.1466 -4.3676 -0.13641 -0.19163 -0.34159 0.012281 0.0027516 0.0047688 0.00029997 0.00033369 0.00029997 -5.1213e-05 -1.8439e-05 -1.493e-05 2.3488e-06 0.32903 -7.4687 -1.0218 -2.7615 -4.2951 -0.2358 -0.38368 -0.30547 0.01014 0.0015708 0.0054265 0.00052811 0.00057802 0.00022698 -5.4663e-05 -2.4405e-05 -1.3018e-05 2.2311e-06 5.3129 5.2474 0.51124 4.0706 1.8134 0.13286 0.47739 0.09974 -0.0061201 0.00042856 -0.0029269 -0.00041147 -0.00066299 -2.0474e-05 3.2549e-05 2.1629e-05 3.2819e-06 -1.1026e-06 -0.022861 1.982 -1.7925 1.6739 0.91205 -0.3483 0.23354 0.058521 -0.016274 0.0018952 -0.0010447 0.0004547 -0.00037767 -3.1309e-05 1.4228e-05 9.7657e-06 1.7938e-06 -1.0894e-06 5.1256 3.9893 -0.53001 2.3454 1.1321 -0.10589 0.26266 0.060274 -0.0097684 0.00011004 -0.0016495 8.0342e-05 -0.00037582 -1.7179e-05 1.7691e-05 1.2126e-05 1.9132e-06 -9.1744e-07 mInv - transition from new to old coordinates 18 -3.5407e-09 -2.8414e-08 1.0653e-07 9.773e-08 8.9555e-07 -4.2148e-06 -3.0672e-06 3.0357e-05 -0.00017671 8.9933e-05 0.0012325 -0.0087008 -0.0019437 -0.16224 0.20301 0.037325 -0.10443 0.16858 -3.3689e-08 1.6936e-07 1.8803e-07 8.9899e-07 -6.2462e-06 -5.3081e-06 -2.3361e-05 -0.00023232 -0.00013094 0.00056286 -0.0090788 -0.0014768 -0.0098182 0.48112 -0.59633 -0.51304 -0.098583 0.4936 1.8663e-07 2.2276e-07 9.9172e-07 -6.4561e-06 -6.1901e-06 -2.4413e-05 0.00021976 -0.00015662 -0.00054205 -0.0073738 -0.0033488 -0.0092314 0.19949 0.068538 -0.11629 0.27005 -0.39934 -0.28531 2.2016e-07 9.7107e-07 -6.1781e-06 -5.7733e-06 -2.2268e-05 0.00019541 0.00013362 -0.00044805 0.0058585 -0.0024502 -0.0063911 0.12497 0.015581 -0.045715 0.20257 0.65367 0.28419 -0.6824 9.1408e-07 -5.7231e-06 -5.2685e-06 -1.9881e-05 0.00017118 0.00011467 0.00037079 0.0047557 0.0019386 -0.0046626 0.090579 0.011228 0.011553 -0.8473 0.72946 0.43551 0.075233 -0.36402 -5.2098e-06 -4.7227e-06 -1.7493e-05 0.00014889 9.8089e-05 0.00031104 -0.0039072 0.0015629 0.0036613 0.068895 0.0084778 0.0078191 -0.97407 -0.0033056 0.016733 -0.13946 0.14268 0.14593 -4.2043e-06 -1.55e-05 0.00012954 8.4174e-05 0.00026314 -0.0032563 -0.001281 0.002946 -0.054293 0.0064942 0.0057937 -0.98884 0.0092756 0.026024 -0.05937 -0.14724 -0.072943 0.15441 -1.3728e-05 0.00011322 7.2751e-05 0.00022537 -0.0027504 -0.0010684 -0.0024225 -0.04394 -0.0051529 0.0044877 -0.99386 0.0065375 0.010915 0.12868 -0.11161 -0.05874 -0.012308 0.047411 9.95e-05 6.3257e-05 0.00019308 -0.0023512 -0.00090432 -0.0020273 0.036311 -0.0041923 -0.0035773 -0.99633 0.0049558 0.0082013 0.10273 -0.0064637 0.0046011 0.024615 -0.016386 -0.025038 5.5322e-05 0.00016921 -0.0020301 -0.00077499 -0.0017218 0.030521 0.0034794 -0.002928 0.99766 0.0039426 0.0063883 0.077715 -0.006448 -0.0057163 0.0092339 0.017316 0.0093535 -0.017808 0.00014911 -0.001771 -0.0006708 -0.0014855 0.026019 0.0029349 0.0024418 0.99844 -0.0032025 0.0051022 0.060626 -0.0048198 -0.0032623 -0.013174 0.01122 0.0049516 0.0012244 -0.0037311 -0.0015583 -0.00058611 -0.0012769 0.022448 0.0025096 0.0020589 -0.99891 -0.0026517 -0.0041649 0.048584 -0.0037449 -0.0024304 -0.010048 0.0012245 -0.0010367 -0.0028376 0.0013362 0.0028405 -0.00051629 -0.0011323 0.019521 0.0021755 0.0017581 -0.99922 0.002235 -0.0034637 -0.039804 -0.0029995 -0.001878 -0.0073445 0.0010057 0.00067825 -0.00095945 -0.0014873 -0.00089078 0.0015102 -0.0010071 0.017171 0.0018793 0.0017026 -0.99943 0.001899 0.0029322 -0.033207 0.0024568 -0.001496 -0.0055954 0.00071744 0.00039313 0.0010279 -0.00086164 -0.00029938 -8.8607e-05 0.0001989 0.015222 0.0016543 0.0010308 -0.99957 0.0016343 0.0024909 0.028129 0.0020498 0.0012194 -0.0044119 0.00053759 0.0002772 0.00074002 -0.00014461 0.00012844 0.00025526 -8.5428e-05 -0.00025206 0.0013653 0.0013196 -0.9998 0.0014823 0.0021876 0.024185 -0.0017416 0.0010175 0.0035775 0.00041943 0.00020559 0.00051518 -0.00010804 -6.1219e-05 7.9952e-05 0.00010529 7.0451e-05 -0.00010548 0.0015032 -0.99985 0.0012546 0.0019127 0.020974 -0.0014927 -0.00086131 0.0029608 -0.0003363 0.00015839 0.00037678 -7.401e-05 -3.5507e-05 -6.8512e-05 5.6268e-05 1.3441e-05 5.043e-06 -6.348e-06 -0.99988 0.0011084 0.0016803 0.018365 -0.0012953 -0.00073703 -0.0024939 -0.00027618 -0.00012576 0.00028733 -5.3538e-05 -2.4169e-05 -4.7809e-05 1.3315e-05 -1.2048e-05 -1.957e-05 4.6024e-06 1.9095e-05 Log norm =-6.71836e-02 for coord=18 l_i :-7.95843e+03 -6.28435e+03 -4.88949e+03 -3.79825e+03 -2.85726e+03 -2.10023e+03 -1.51087e+03 -1.04751e+03 -6.97713e+02 -4.42531e+02 -2.62270e+02 -1.41346e+02 -6.50763e+01 -1.60651e+01 -1.08056e+01 -4.01045e+00 -4.01045e+00 -6.71836e-02 -9.82019e+03 -1.21436e+04 -1.48489e+04 -1.79782e+04 -2.15676e+04 -2.56630e+04 -3.03098e+04 -3.55544e+04 -4.14460e+04 -4.80356e+04 -5.53760e+04 -6.35220e+04 -7.25300e+04 -8.24588e+04 -9.33688e+04 -1.05322e+05 -1.18384e+05 -1.32620e+05 -1.48098e+05 diff. estm L2=3.62418e-03 H1=1.40165e-02 C0=4.99777e-03 C1=2.00351e-02 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-3.28053e-05,-3.04044e-05] +[-8.07296e+03,-8.07275e+03]x_{1} \\ x'_{2}&=&[-4.30997e-05,-4.02577e-05] +[-6.39146e+03,-6.39129e+03]x_{2} \\ x'_{3}&=&[-1.47960e-04,-1.40648e-04] +[-4.98556e+03,-4.98543e+03]x_{3} \\ x'_{4}&=&[7.09062e-06,2.56384e-05] +[-3.82475e+03,-3.82464e+03]x_{4} \\ x'_{5}&=&[3.32620e-06,1.80541e-05] +[-2.87698e+03,-2.87690e+03]x_{5} \\ x'_{6}&=&[1.82408e-06,3.54725e-05] +[-2.11551e+03,-2.11546e+03]x_{6} \\ x'_{7}&=&[-6.46057e-05,5.99870e-05] +[-1.51446e+03,-1.51441e+03]x_{7} \\ x'_{8}&=&[-3.31630e-05,3.62286e-05] +[-1.04976e+03,-1.04973e+03]x_{8} \\ x'_{9}&=&[-6.40169e-05,6.55145e-05] +[-6.99355e+02,-6.99335e+02]x_{9} \\ x'_{10}&=&[-2.82867e-04,2.85316e-04] +[-4.43062e+02,-4.43049e+02]x_{10} \\ x'_{11}&=&[-9.58947e-05,9.90658e-05] +[-2.62607e+02,-2.62599e+02]x_{11} \\ x'_{12}&=&[-1.32043e-04,1.32151e-04] +[-1.41607e+02,-1.41602e+02]x_{12} \\ x'_{13}&=&[-6.73810e-04,6.71949e-04] +[-6.52455e+01,-6.52425e+01]x_{13} \\ x'_{14}&=&[-5.93751e-04,5.93460e-04] +[-1.67452e+01,-1.67401e+01]x_{14} \\ x'_{15}&=&[-8.20396e-04,8.23276e-04] +[-1.16759e+01,-1.16711e+01]x_{15} \\ x'_{16}&=&[-5.52558e-04,5.49865e-04] +[-4.74363e+00,-4.74073e+00]x_{16} +[2.18347e+00,2.18451e+00]x_{17} \\ x'_{17}&=&[-6.71552e-04,6.72347e-04] +[-2.18474e+00,-2.18325e+00]x_{16} +[-4.74251e+00,-4.74184e+00]x_{17} \\ x'_{18}&=&[-3.81583e-04,3.80949e-04] +[-5.64830e-01,-5.63144e-01]x_{18} \\ \end{eqnarray*} ************************** a trimodal fixed point nu= 0.062+[-1e-06,1e-06] alpha=[64.5151,64.5172] dimensions m= 15 M=30 delta=0.00025 number of iterates=8 starting point : 0 0 2.25835 0 0 -0.640352 0 0 0.0788756 0 0 -0.00802132 0 0 0.000706544 fixed point : 2.71998e-19 -3.5786e-19 2.25835 -2.08944e-18 1.65509e-18 -0.640352 1.10899e-17 -1.25244e-17 0.0788755 -4.05546e-18 3.34702e-18 -0.0080206 7.57199e-19 -5.74621e-19 0.000705167 difference fixed - starting : 2.71998e-19 -3.5786e-19 -6.87355e-08 -2.08944e-18 1.65509e-18 -5.79025e-08 1.10899e-17 -1.25244e-17 -1.08158e-07 -4.05546e-18 3.34702e-18 7.1662e-07 7.57199e-19 -5.74621e-19 -1.37686e-06 Isolating neighborhood (the set N):[-1.318857e-11,1.318857e-11] [-1.367412e-06,-1.334389e-06] [-2.574707e-11,2.574707e-11] [-5.550619e-12,5.550614e-12] [-1.251859e-11,1.251860e-11] [-8.623991e-12,8.623966e-12] [-8.600933e-07,-4.859545e-07] [-2.128985e-06,1.974484e-06] [-2.331317e-11,2.331315e-11] [-4.404132e-10,4.404132e-10] [-4.404132e-10,4.404132e-10] [-2.964121e-08,2.964121e-08] [-2.964121e-08,2.964121e-08] [-3.664279e-05,3.697187e-05] [-8.458770e-05,8.488539e-05] W=2.719985e-19+[-9.691500e-09,9.691500e-09] -3.578599e-19+[-1.584934e-08,1.584934e-08] 2.258346e+00+[-8.338196e-05,8.338196e-05] -2.089436e-18+[-2.964115e-08,2.964115e-08] 1.655091e-18+[-2.071243e-08,2.071243e-08] -6.403523e-01+[-8.043257e-05,8.043257e-05] 1.108986e-17+[-9.682567e-09,9.682567e-09] -1.252444e-17+[-4.690581e-09,4.690581e-09] 7.887548e-02+[-1.559258e-05,1.559258e-05] -4.055457e-18+[-1.593809e-09,1.593809e-09] 3.347021e-18+[-7.035628e-10,7.035628e-10] -8.020604e-03+[-2.210283e-06,2.210283e-06] 7.571995e-19+[-2.240510e-10,2.240510e-10] -5.746215e-19+[-9.464340e-11,9.464340e-11] 7.051670e-04+[-2.493346e-07,2.493346e-07] ------------------------------------- Self-consistent bounds k=1 b=2.719985e-19+[-9.691500e-09,9.691500e-09] k=2 b=-3.578599e-19+[-1.584934e-08,1.584934e-08] k=3 b=2.258346e+00+[-8.338196e-05,8.338196e-05] k=4 b=-2.089436e-18+[-2.964115e-08,2.964115e-08] k=5 b=1.655091e-18+[-2.071243e-08,2.071243e-08] k=6 b=-6.403523e-01+[-8.043257e-05,8.043257e-05] k=7 b=1.108986e-17+[-9.682567e-09,9.682567e-09] k=8 b=-1.252444e-17+[-4.690581e-09,4.690581e-09] k=9 b=7.887548e-02+[-1.559258e-05,1.559258e-05] k=10 b=-4.055457e-18+[-1.593809e-09,1.593809e-09] k=11 b=3.347021e-18+[-7.035628e-10,7.035628e-10] k=12 b=-8.020604e-03+[-2.210283e-06,2.210283e-06] k=13 b=7.571995e-19+[-2.240510e-10,2.240510e-10] k=14 b=-5.746215e-19+[-9.464340e-11,9.464340e-11] k=15 b=7.051670e-04+[-2.493346e-07,2.493346e-07] k=16 b=-8.982428e-20+[-1.197160e-10,1.197160e-10] k=17 b=3.079965e-20+[-6.477598e-11,6.477598e-11] k=18 b=-5.721503e-05+[-2.380867e-08,2.380867e-08] k=19 b=5.396113e-21+[-5.060623e-10,5.060623e-10] k=20 b=-6.040409e-21+[-3.073947e-10,3.073947e-10] k=21 b=4.384282e-06+[-2.341631e-09,2.341631e-09] k=22 b=-9.198249e-22+[-2.773167e-09,2.773167e-09] k=23 b=3.127777e-22+[-1.750903e-09,1.750903e-09] k=24 b=-3.223467e-07+[-1.305868e-09,1.305868e-09] k=25 b=4.714930e-23+[-1.453796e-08,1.453796e-08] k=26 b=-5.128520e-23+[-9.390004e-09,9.390004e-09] k=27 b=2.296173e-08+[-6.168501e-09,6.168501e-09] k=28 b=-9.926168e-24+[-3.816283e-08,3.816283e-08] k=29 b=1.654362e-24+[-2.504385e-08,2.504385e-08] k=30 b=-1.595663e-09+[-1.665755e-08,1.665755e-08] Tail : 8.239381e+09/k^10 ------------------------------------- Galerkin errors (epsilons) k=1 -1.309531e-22+[-6.813914e-10,6.813914e-10] k=2 1.089811e-22+[-1.002752e-09,1.002752e-09] k=3 -2.435906e-07+[-1.305635e-09,1.305635e-09] k=4 6.060236e-21+[-1.130093e-09,1.130093e-09] k=5 -2.951174e-21+[-1.063840e-09,1.063840e-09] k=6 5.544112e-06+[-4.807403e-09,4.807403e-09] k=7 -1.025415e-19+[-1.137784e-09,1.137784e-09] k=8 4.342378e-20+[-9.499186e-10,9.499186e-10] k=9 -8.186861e-05+[-5.109385e-08,5.109385e-08] k=10 1.173826e-18+[-4.514542e-09,4.514542e-09] k=11 -4.588537e-19+[-3.169932e-09,3.169932e-09] k=12 8.876685e-04+[-4.838316e-07,4.838316e-07] k=13 -5.370077e-18+[-4.070747e-08,4.070747e-08] k=14 2.061416e-18+[-2.855365e-08,2.855365e-08] k=15 -3.961332e-03+[-1.826627e-06,1.826627e-06] ------------------------------------- shift 0.000000e+00 0.000000e+00 2.258346e+00 0.000000e+00 0.000000e+00 -6.403522e-01 0.000000e+00 0.000000e+00 7.887558e-02 0.000000e+00 0.000000e+00 -8.021321e-03 0.000000e+00 0.000000e+00 7.065438e-04 m - transition from old to new coordinates 15 -9.8855e-07 2.3709e-05 0 1.0309e-06 -0.00059303 0 -7.856e-08 0.0078855 0 7.629e-09 -0.045584 0 -3.0915e-09 -1.0023 0 0 0 -2.7295e-05 0 0 0.00052636 0 0 -0.0066404 0 0 0.038497 0 0 1.0017 -1.6043e-05 2.6796e-06 0 0.0006594 -1.3272e-06 0 -0.0094953 -3.3266e-06 0 0.054864 3.1209e-05 0 1.0032 0.00030136 0 3.384e-05 -0.00071196 0 -1.051e-05 0.014416 0 3.659e-06 -0.083682 0 -1.1522e-06 -1.0098 0 -1.1524e-07 -0.035217 0 -0.00055869 0.00010224 0 0.018278 -2.1182e-05 0 -0.10856 9.6956e-06 0 -1.0152 2.3165e-06 0 -0.041436 -3.2343e-09 0 0.0016739 -0.030355 0 -0.00058469 0.21317 0 0.00033733 1.0459 0 4.9607e-05 0.061245 0 -8.95e-07 -0.0037565 0 0 0 -0.00071872 0 0 0.011585 0 0 -0.066609 0 0 -1.0066 0 0 -0.030336 0 0 -0.023796 0 0 0.14719 0 0 1.0252 0 0 0.049893 0 0 -0.0034654 0.035829 -0.006849 0 -0.3477 0.0029083 0 -1.0988 0.001071 0 -0.078537 2.2622e-05 0 0.0040437 -3.4881e-06 0 -0.40363 0.80444 0 0.65134 -0.47525 0 0.1405 -0.079342 0 0.0020208 0.00059682 0 -0.00047047 0.00020411 0 -0.46863 1.522 0 -0.19573 1.2571 0 -0.013039 0.13232 0 0.00097167 -0.0035527 0 2.7842e-05 -0.00027028 0 -1.0198 -0.63999 0 -1.3996 -0.52416 0 -0.24552 -0.056118 0 -0.0014903 0.0014501 0 0.00079064 0.00011584 0 3.2516 1.9241 0 0.64743 0.63728 0 0.067105 0.051151 0 -0.0014184 -0.0021107 0 -0.00018678 -8.3609e-05 0 0 0 -0.92947 0 0 -1.4455 0 0 -0.12498 0 0 0.0050555 0 0 0.00013604 0 0 -1.5875 0 0 -0.59845 0 0 -0.032151 0 0 0.002238 0 0 6.3235e-07 mInv - transition from new to old coordinates 15 1.6984e-06 0 2.1302e-05 -5.319e-05 0.00059963 -0.0021934 0 0 -0.021798 -0.22421 -0.19818 0.052735 0.26793 0 0 -2.8708e-05 0 -5.0309e-06 0.00071345 -0.00017952 0.01956 0 0 0.0099478 0.55994 0.23807 0.31907 0.20377 0 0 0 3.0303e-05 0 0 0 0 0.0006907 0.016166 0 0 0 0 0 0.34655 -0.83309 -6.4844e-07 0 -0.00060418 2.3658e-05 -0.012496 0.001084 0 0 0.18323 0.19451 -0.12534 -0.76061 -0.23449 0 0 0.00052733 0 8.4681e-07 -0.010069 4.4979e-05 -0.12854 0 0 -0.001977 -0.75011 0.42261 -0.4942 -0.18711 0 0 0 -0.00045789 0 0 0 0 -0.0082446 -0.096473 0 0 0 0 0 -0.92697 0.5442 2.1079e-06 0 0.0068365 -1.7316e-06 0.075336 8.2574e-05 0 0 -0.97666 -0.075018 0.033169 0.24208 0.082166 0 0 -0.0057671 0 -7.035e-08 0.060623 5.1136e-07 0.98786 0 0 0.0011469 0.17112 -0.079727 0.11037 0.043845 0 0 0 0.0049268 0 0 0 0 0.049896 0.9929 0 0 0 0 0 0.14213 -0.098123 -1.2459e-05 0 -0.041521 -1.4876e-06 -0.99555 2.5755e-05 0 0 0.10838 0.011782 -0.0057089 -0.03977 -0.013199 0 0 0.035339 0 -1.3226e-08 -0.99706 2.2846e-06 -0.08412 0 0 -0.00013717 -0.025397 0.012517 -0.016483 -0.0064629 0 0 0 -0.030453 0 0 0 0 -0.99797 -0.067099 0 0 0 0 0 -0.020387 0.013395 0.00029978 0 0.99911 1.7485e-05 0.055165 7.8887e-07 0 0 -0.015291 -0.0014878 0.00070505 0.0049657 0.0016572 0 0 -0.99936 0 -5.148e-09 0.045829 -1.5784e-07 0.011674 0 0 1.6954e-05 0.0029588 -0.0014409 0.0019171 0.00075389 0 0 0 0.99952 0 0 0 0 0.03869 0.0092121 0 0 0 0 0 0.0022223 -0.0014739 Log norm =-1.10448e-02 for coord=12 l_i :-2.09884e+03 -2.82110e+03 -1.52025e+03 -7.66591e+02 -5.00763e+02 -1.85447e+02 -1.12044e+03 -3.21665e+02 -9.45420e+01 -9.90762e+00 -9.90762e+00 -1.10448e-02 -1.10448e-02 -3.85282e+01 -9.32055e+00 -3.60462e+03 -4.67594e+03 -5.96135e+03 -7.48920e+03 -9.27870e+03 -1.13640e+04 -1.37767e+04 -1.65461e+04 -1.97071e+04 -2.32950e+04 -2.73459e+04 -3.18978e+04 -3.69902e+04 -4.26640e+04 -4.89616e+04 -5.59268e+04 diff. estm L2=4.66307e-04 H1=4.61791e-03 C0=5.85777e-04 C1=7.27664e-03 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-2.87961e-08,2.87961e-08] +[-2.18349e+03,-2.18341e+03]x_{1} \\ x'_{2}&=&[-3.98127e-03,-3.88526e-03] +[-2.91164e+03,-2.91154e+03]x_{2} \\ x'_{3}&=&[-4.11747e-08,4.11747e-08] +[-1.59926e+03,-1.59920e+03]x_{3} \\ x'_{4}&=&[-4.36193e-09,4.36193e-09] +[-7.85876e+02,-7.85846e+02]x_{4} \\ x'_{5}&=&[-6.49606e-09,6.49606e-09] +[-5.18933e+02,-5.18913e+02]x_{5} \\ x'_{6}&=&[-1.62341e-09,1.62341e-09] +[-1.88253e+02,-1.88244e+02]x_{6} \\ x'_{7}&=&[-9.81258e-04,-5.54433e-04] +[-1.14092e+03,-1.14087e+03]x_{7} \\ x'_{8}&=&[-6.90846e-04,6.40711e-04] +[-3.24509e+02,-3.24496e+02]x_{8} \\ x'_{9}&=&[-2.27042e-09,2.27042e-09] +[-9.73933e+01,-9.73879e+01]x_{9} \\ x'_{10}&=&[-2.62034e-09,2.62034e-09] +[-1.01186e+01,-1.01179e+01]x_{10} +[1.01658e+01,1.01662e+01]x_{11} \\ x'_{11}&=&[-3.60370e-09,3.60370e-09] +[-1.01667e+01,-1.01653e+01]x_{10} +[-1.01187e+01,-1.01179e+01]x_{11} \\ x'_{12}&=&[-3.86848e-09,3.86848e-09] +[-2.34646e-01,-2.33432e-01]x_{12} +[5.96502e+00,5.96544e+00]x_{13} \\ x'_{13}&=&[-5.71520e-09,5.71520e-09] +[-5.96563e+00,-5.96483e+00]x_{12} +[-2.34183e-01,-2.33896e-01]x_{13} \\ x'_{14}&=&[-1.42894e-03,1.44177e-03] +[-3.90002e+01,-3.89965e+01]x_{14} \\ x'_{15}&=&[-8.02739e-04,8.05564e-04] +[-9.49112e+00,-9.49002e+00]x_{15} \\ \end{eqnarray*} **************** a fixed point from giant branch nu= 0.062+[-1e-06,1e-06] alpha=[64.5151,64.5172] dimensions m= 12 M=24 delta=0.00125 number of iterates=8 starting point : 0.770939 -1.22918 -0.317306 -0.948735 0.0827463 -0.320163 -0.000178026 -0.0670203 0.000953438 -0.0148681 0.000434386 -0.00279872 fixed point : 0.770947 -1.22919 -0.317304 -0.948742 0.0827504 -0.320168 -0.000178272 -0.0670108 0.000947681 -0.01485 0.000435852 -0.00278255 difference fixed - starting : 8.33178e-06 -1.02823e-05 1.45522e-06 -7.58187e-06 4.08519e-06 -5.18938e-06 -2.4574e-07 9.51429e-06 -5.75663e-06 1.80823e-05 1.46605e-06 1.61685e-05 Isolating neighborhood (the set N):[1.524414e-05,1.552994e-05] [-3.630155e-06,-3.341926e-06] [1.669708e-05,1.764331e-05] [3.697904e-06,4.429576e-06] [-1.173416e-05,-7.421237e-06] [-1.347218e-06,2.482569e-06] [-1.766123e-05,2.027707e-05] [-9.376794e-05,9.376794e-05] [-9.377777e-05,9.377777e-05] [-3.119537e-04,3.119537e-04] [-3.119367e-04,3.119367e-04] [-1.463529e-04,1.122959e-04] W=7.709472e-01+[-2.882010e-04,2.882010e-04] -1.229190e+00+[-3.893475e-04,3.893475e-04] -3.173045e-01+[-3.735537e-04,3.735537e-04] -9.487424e-01+[-3.698051e-04,3.698051e-04] 8.275038e-02+[-3.178709e-04,3.178709e-04] -3.201678e-01+[-2.008147e-04,2.008147e-04] -1.782718e-04+[-1.108880e-04,1.108880e-04] -6.701079e-02+[-5.801429e-05,5.801429e-05] 9.476809e-04+[-3.137949e-05,3.137949e-05] -1.484997e-02+[-1.610987e-05,1.610987e-05] 4.358524e-04+[-8.042733e-06,8.042733e-06] -2.782555e-03+[-3.830210e-06,3.830210e-06] ------------------------------------- Self-consistent bounds k=1 b=7.709472e-01+[-2.882010e-04,2.882010e-04] k=2 b=-1.229190e+00+[-3.893475e-04,3.893475e-04] k=3 b=-3.173045e-01+[-3.735537e-04,3.735537e-04] k=4 b=-9.487424e-01+[-3.698051e-04,3.698051e-04] k=5 b=8.275038e-02+[-3.178709e-04,3.178709e-04] k=6 b=-3.201678e-01+[-2.008147e-04,2.008147e-04] k=7 b=-1.782718e-04+[-1.108880e-04,1.108880e-04] k=8 b=-6.701079e-02+[-5.801429e-05,5.801429e-05] k=9 b=9.476809e-04+[-3.137949e-05,3.137949e-05] k=10 b=-1.484997e-02+[-1.610987e-05,1.610987e-05] k=11 b=4.358524e-04+[-8.042733e-06,8.042733e-06] k=12 b=-2.782555e-03+[-3.830210e-06,3.830210e-06] k=13 b=6.456679e-05+[-1.923526e-06,1.923526e-06] k=14 b=-4.973197e-04+[-8.672952e-07,8.672952e-07] k=15 b=1.490434e-05+[-4.163472e-07,4.163472e-07] k=16 b=-8.620094e-05+[-1.915923e-07,1.915923e-07] k=17 b=2.836029e-06+[-1.623857e-07,1.623857e-07] k=18 b=-1.433910e-05+[-8.978553e-08,8.978553e-08] k=19 b=5.126052e-07+[-2.852227e-07,2.852227e-07] k=20 b=-2.335747e-06+[-2.305551e-07,2.305551e-07] k=21 b=9.232635e-08+[-6.481279e-07,6.481279e-07] k=22 b=-3.727354e-07+[-5.600330e-07,5.600330e-07] k=23 b=1.592166e-08+[-8.530284e-07,8.530284e-07] k=24 b=-5.849537e-08+[-8.232372e-07,8.232372e-07] Tail : 2.228157e+07/k^8 ------------------------------------- Galerkin errors (epsilons) k=1 -4.415432e-07+[-1.621521e-07,1.621521e-07] k=2 5.828507e-06+[-2.435872e-07,2.435872e-07] k=3 -7.345965e-06+[-4.604052e-07,4.604052e-07] k=4 6.160267e-05+[-4.580459e-07,4.580459e-07] k=5 -5.066136e-05+[-1.811704e-06,1.811704e-06] k=6 4.158084e-04+[-1.426548e-06,1.426548e-06] k=7 -3.040004e-04+[-1.030680e-05,1.030680e-05] k=8 2.729052e-03+[-9.489544e-06,9.489544e-06] k=9 -1.932854e-03+[-4.078345e-05,4.078345e-05] k=10 9.623388e-03+[-3.583812e-05,3.583812e-05] k=11 1.236821e-03+[-7.629204e-05,7.629204e-05] k=12 1.783488e-02+[-7.824403e-05,7.824403e-05] ------------------------------------- Coordinate change: shift 7.709388e-01 -1.229179e+00 -3.173060e-01 -9.487348e-01 8.274629e-02 -3.201626e-01 -1.780260e-04 -6.702030e-02 9.534375e-04 -1.486805e-02 4.343863e-04 -2.798723e-03 m - transition from old to new coordinates 12 6.5606e-07 -0.00010069 -1.394e-05 -0.00079295 -0.00018548 -0.0056714 0.0011454 -0.023613 -0.011759 -0.047088 0.053911 1.007 7.5017e-05 1.7521e-05 0.00090519 0.00029557 0.0070434 -0.00099174 0.029896 0.017041 0.059273 -0.061304 -1.0147 -0.045579 -2.0082e-05 -0.00097046 -0.00043456 -0.0088892 0.00088881 -0.038824 -0.023978 -0.073144 0.077077 1.0257 0.057728 -0.037647 0.00095563 0.00065171 0.011418 -0.00051465 0.053551 0.035378 0.096649 -0.10168 -1.042 -0.069882 0.045105 0.012184 0.00090864 0.015097 0.00069512 0.079315 0.057811 0.13426 -0.13816 -1.0757 -0.089277 0.057466 0.016416 0.015728 0.020059 0.0050977 0.1357 0.11205 0.20823 -0.20711 -1.1553 -0.12165 0.075437 0.024875 0.019958 0.00051773 0.031466 0.34111 0.32543 0.42934 -0.39438 -1.4454 -0.19821 0.11464 0.046856 0.029781 0.0015158 0.0021467 -1.9821 -1.7626 -1.1766 -0.11346 0.070345 0.19648 0.11383 0.0082203 -0.0010765 -0.0039886 -0.0013651 -0.00044979 -1.3174 -1.5035 -0.99737 1.2836 2.3784 0.40024 -0.2374 -0.13003 -0.058687 -0.0051851 -0.0022546 -2.4174e-05 -1.0163 -1.0811 1.0242 0.29908 -0.54884 -0.060626 0.011422 0.015108 0.012016 -0.000857 0.001033 -9.6499e-05 0.32841 -0.65322 -0.3093 1.5459 0.51373 -0.20684 -0.1036 -0.055863 -0.0040465 0.0009973 2.7187e-05 0.00063918 -0.18104 0.9712 1.5009 1.2019 -0.26491 -0.49105 -0.12558 -0.016044 0.013147 0.0059663 0.0016594 0.00096536 mInv - transition from new to old coordinates 12 -3.3766e-06 -9.6545e-05 -4.9257e-05 -0.00106 0.00081429 -0.015152 0.028835 -0.47147 -0.060072 0.21304 0.34677 -0.48832 0.0001006 4.0633e-05 0.00096725 0.00053297 -0.011176 0.012703 -0.12577 0.28118 -0.063116 -0.65312 -0.2341 0.60207 -2.3713e-05 -0.00081702 -0.00033855 -0.0083271 0.0071443 -0.066088 0.048323 -0.5206 0.22975 0.63953 -0.29163 -0.090151 0.00069941 0.00023204 0.0064772 0.0045914 -0.044267 0.0098627 -0.24376 0.30135 -0.18195 -0.25349 0.58082 0.45996 -0.00011097 -0.0051367 -0.0032117 -0.032652 -0.00029908 -0.15208 0.25076 -0.51306 0.59095 0.14194 -0.43127 -0.23562 0.0042033 0.0024066 0.025291 -0.0035367 -0.10662 0.17107 -0.89063 0.19494 -0.20265 -0.13811 0.19334 0.32997 -0.0015762 -0.019952 0.0044113 -0.079387 0.12365 -0.95341 0.20287 -0.17453 0.15712 0.10888 -0.093272 -0.083157 0.016354 -0.0045209 0.061736 0.093606 -0.9759 0.14521 -0.14744 0.04924 -0.032182 -0.053568 0.056302 0.083976 0.0053481 -0.04812 -0.073665 -0.98638 0.10821 -0.10706 0.019747 -0.048308 0.045045 0.025864 -0.03454 -0.019846 0.040152 0.060976 0.99157 0.082376 -0.080205 0.0049171 -0.044397 0.014351 -0.012512 -0.011571 0.017421 0.023265 -0.046716 -0.99521 -0.065361 -0.063502 -0.00031003 -0.033762 0.010426 -0.012314 0.012049 0.0062726 -0.0082917 -0.0057803 0.99794 0.055501 0.050598 -0.0020038 -0.026132 0.0062204 -0.011266 0.0033814 -0.0028164 -0.0029628 0.0037208 0.005466 Log norm =-1.31478e+00 for coord=10 l_i :-1.04244e+03 -7.09879e+02 -4.72855e+02 -2.89484e+02 -1.72406e+02 -8.58975e+01 -3.47263e+01 -6.95707e+00 -6.95707e+00 -1.31478e+00 -1.31478e+00 -1.47104e+00 -1.38297e+03 -1.95862e+03 -2.67661e+03 -3.55480e+03 -4.62856e+03 -5.91050e+03 -7.43212e+03 -9.21848e+03 -1.13008e+04 -1.37089e+04 -1.64753e+04 -1.96332e+04 -2.32167e+04 diff. estm L2=3.58514e-03 H1=3.62529e-02 C0=7.28128e-03 C1=7.65059e-02 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[1.73653e-02,1.76903e-02] +[-1.13915e+03,-1.13911e+03]x_{1} \\ x'_{2}&=&[-2.84907e-03,-2.62296e-03] +[-7.84864e+02,-7.84834e+02]x_{2} \\ x'_{3}&=&[8.66653e-03,9.15729e-03] +[-5.19044e+02,-5.19024e+02]x_{3} \\ x'_{4}&=&[1.20050e-03,1.43798e-03] +[-3.24644e+02,-3.24630e+02]x_{4} \\ x'_{5}&=&[-2.21628e-03,-1.40175e-03] +[-1.88883e+02,-1.88875e+02]x_{5} \\ x'_{6}&=&[-1.32409e-04,2.43995e-04] +[-9.82889e+01,-9.82832e+01]x_{6} \\ x'_{7}&=&[-7.34098e-04,8.42827e-04] +[-4.15694e+01,-4.15655e+01]x_{7} \\ x'_{8}&=&[-1.74325e-04,1.98939e-04] +[-8.87453e+00,-8.87415e+00]x_{8} +[6.52653e+00,6.52683e+00]x_{9} \\ x'_{9}&=&[-8.07833e-04,6.11485e-04] +[-6.52888e+00,-6.52657e+00]x_{8} +[-8.87585e+00,-8.87347e+00]x_{9} \\ x'_{10}&=&[-1.70962e-04,1.97931e-04] +[-2.15301e+00,-2.15271e+00]x_{10} +[1.03724e+01,1.03729e+01]x_{11} \\ x'_{11}&=&[-6.41413e-04,4.19936e-04] +[-1.03717e+01,-1.03712e+01]x_{10} +[-2.15331e+00,-2.15238e+00]x_{11} \\ x'_{12}&=&[-6.55123e-04,5.02673e-04] +[-4.47721e+00,-4.47632e+00]x_{12} \\ \end{eqnarray*} ******************** a fixed point from giant branch nu= 0.045+[-1e-06,1e-06] alpha=[88.8869,88.8909] dimensions m= 20 M=40 delta=0.00125 number of iterates=8 starting point : 1.02378 -1.21449 -0.376932 -1.01602 0.0413416 -0.57969 0.0280282 -0.15565 -0.00203885 -0.0427612 0.000974983 -0.0114576 0.000344454 -0.0026841 6.11398e-05 -0.000611992 1.78779e-05 -0.00013718 4.55392e-06 -2.97065e-05 fixed point : 1.02378 -1.21449 -0.376932 -1.01602 0.0413416 -0.57969 0.0280282 -0.15565 -0.00203884 -0.0427612 0.000974991 -0.0114576 0.000344454 -0.00268409 6.11293e-05 -0.000611947 1.78633e-05 -0.000137124 4.55931e-06 -2.96464e-05 difference fixed - starting : 5.29999e-10 -8.57051e-10 1.57807e-09 -1.68849e-09 2.87942e-09 -4.89599e-09 1.11116e-08 -1.56109e-08 1.4772e-08 -1.14416e-08 7.23183e-09 3.84117e-11 -7.1123e-11 1.50312e-08 -1.05072e-08 4.45583e-08 -1.45772e-08 5.57528e-08 5.39506e-09 6.00651e-08 Isolating neighborhood (the set N):[-6.100512e-08,-5.664303e-08] [7.363945e-09,1.116334e-08] [-5.956699e-08,-4.726489e-08] [6.453661e-09,1.544349e-08] [1.802866e-08,6.547185e-08] [-6.760653e-09,2.278102e-08] [-1.139919e-07,8.762617e-08] [-6.330204e-08,6.371087e-08] [-4.360628e-07,4.350648e-07] [-2.843915e-07,2.744223e-07] [-1.810514e-06,1.827324e-06] [-1.509117e-06,1.489007e-06] [-9.259369e-06,9.283425e-06] [-1.657787e-05,1.656140e-05] [-6.980909e-04,6.980909e-04] [-6.980928e-04,6.980928e-04] [-4.699575e-04,4.699575e-04] [-4.699651e-04,4.699651e-04] [-2.806617e-04,2.806617e-04] [-2.806617e-04,2.806617e-04] W=1.023781e+00+[-5.704057e-04,5.704057e-04] -1.214490e+00+[-1.055210e-03,1.055210e-03] -3.769316e-01+[-9.457494e-04,9.457494e-04] -1.016017e+00+[-1.133483e-03,1.133483e-03] 4.134163e-02+[-1.009418e-03,1.009418e-03] -5.796896e-01+[-9.250807e-04,9.250807e-04] 2.802824e-02+[-5.542214e-04,5.542214e-04] -1.556504e-01+[-3.490182e-04,3.490182e-04] -2.038838e-03+[-1.813643e-04,1.813643e-04] -4.276124e-02+[-1.191683e-04,1.191683e-04] 9.749907e-04+[-6.240988e-05,6.240988e-05] -1.145760e-02+[-3.860570e-05,3.860570e-05] 3.444544e-04+[-1.864895e-05,1.864895e-05] -2.684090e-03+[-1.070847e-05,1.070847e-05] 6.112933e-05+[-4.962013e-06,4.962013e-06] -6.119472e-04+[-2.807462e-06,2.807462e-06] 1.786334e-05+[-1.286968e-06,1.286968e-06] -1.371245e-04+[-7.134750e-07,7.134750e-07] 4.559314e-06+[-3.205411e-07,3.205411e-07] -2.964642e-05+[-1.743751e-07,1.743751e-07] ------------------------------------- Self-consistent bounds k=1 b=1.023781e+00+[-5.704057e-04,5.704057e-04] k=2 b=-1.214490e+00+[-1.055210e-03,1.055210e-03] k=3 b=-3.769316e-01+[-9.457494e-04,9.457494e-04] k=4 b=-1.016017e+00+[-1.133483e-03,1.133483e-03] k=5 b=4.134163e-02+[-1.009418e-03,1.009418e-03] k=6 b=-5.796896e-01+[-9.250807e-04,9.250807e-04] k=7 b=2.802824e-02+[-5.542214e-04,5.542214e-04] k=8 b=-1.556504e-01+[-3.490182e-04,3.490182e-04] k=9 b=-2.038838e-03+[-1.813643e-04,1.813643e-04] k=10 b=-4.276124e-02+[-1.191683e-04,1.191683e-04] k=11 b=9.749907e-04+[-6.240988e-05,6.240988e-05] k=12 b=-1.145760e-02+[-3.860570e-05,3.860570e-05] k=13 b=3.444544e-04+[-1.864895e-05,1.864895e-05] k=14 b=-2.684090e-03+[-1.070847e-05,1.070847e-05] k=15 b=6.112933e-05+[-4.962013e-06,4.962013e-06] k=16 b=-6.119472e-04+[-2.807462e-06,2.807462e-06] k=17 b=1.786334e-05+[-1.286968e-06,1.286968e-06] k=18 b=-1.371245e-04+[-7.134750e-07,7.134750e-07] k=19 b=4.559314e-06+[-3.205411e-07,3.205411e-07] k=20 b=-2.964642e-05+[-1.743751e-07,1.743751e-07] k=21 b=1.030848e-06+[-7.994715e-08,7.994715e-08] k=22 b=-6.287647e-06+[-4.208582e-08,4.208582e-08] k=23 b=2.400201e-07+[-1.842131e-08,1.842131e-08] k=24 b=-1.314975e-06+[-9.604427e-09,9.604427e-09] k=25 b=5.446127e-08+[-4.171357e-09,4.171357e-09] k=26 b=-2.707851e-07+[-2.153531e-09,2.153531e-09] k=27 b=1.197195e-08+[-9.427277e-10,9.427277e-10] k=28 b=-5.509935e-08+[-4.868317e-10,4.868317e-10] k=29 b=2.603774e-09+[-2.551498e-10,2.551498e-10] k=30 b=-1.110259e-08+[-1.441584e-10,1.441584e-10] k=31 b=5.585014e-10+[-1.999389e-10,1.999389e-10] k=32 b=-2.216956e-09+[-1.415309e-10,1.415309e-10] k=33 b=1.181099e-10+[-4.682430e-10,4.682430e-10] k=34 b=-4.392306e-10+[-4.001126e-10,4.001126e-10] k=35 b=2.471802e-11+[-1.436708e-09,1.436708e-09] k=36 b=-8.642910e-11+[-1.120239e-09,1.120239e-09] k=37 b=5.123346e-12+[-2.512463e-09,2.512463e-09] k=38 b=-1.690318e-11+[-2.412698e-09,2.412698e-09] k=39 b=1.052798e-12+[-3.493409e-09,3.493409e-09] k=40 b=-3.288375e-12+[-3.906868e-09,3.906868e-09] Tail : 2.508268e+10/k^10 ------------------------------------- Galerkin errors (epsilons) k=1 -7.795213e-11+[-3.775177e-11,3.775177e-11] k=2 8.001680e-10+[-6.220834e-11,6.220834e-11] k=3 -1.073969e-09+[-1.467798e-10,1.467798e-10] k=4 7.381290e-09+[-1.725560e-10,1.725560e-10] k=5 -7.843326e-09+[-7.029003e-10,7.029003e-10] k=6 4.925428e-08+[-7.385000e-10,7.385000e-10] k=7 -4.664635e-08+[-3.893009e-09,3.893009e-09] k=8 2.894878e-07+[-3.887408e-09,3.887408e-09] k=9 -2.654232e-07+[-2.074835e-08,2.074835e-08] k=10 1.536856e-06+[-1.845821e-08,1.845821e-08] k=11 -1.179162e-06+[-9.325718e-08,9.325718e-08] k=12 6.788162e-06+[-7.454260e-08,7.454260e-08] k=13 -4.158853e-06+[-3.899423e-07,3.899423e-07] k=14 2.986705e-05+[-3.430610e-07,3.430610e-07] k=15 -2.434023e-05+[-1.661714e-06,1.661714e-06] k=16 1.251578e-04+[-1.194129e-06,1.194129e-06] k=17 -5.072717e-05+[-3.507336e-06,3.507336e-06] k=18 2.454530e-04+[-3.218379e-06,3.218379e-06] k=19 2.959100e-05+[-5.455963e-06,5.455963e-06] k=20 4.042371e-04+[-6.419363e-06,6.419363e-06] ------------------------------------- Coordinate change: shift 1.023781e+00 -1.214489e+00 -3.769316e-01 -1.016017e+00 4.134162e-02 -5.796895e-01 2.802822e-02 -1.556504e-01 -2.038852e-03 -4.276123e-02 9.749834e-04 -1.145759e-02 3.444544e-04 -2.684104e-03 6.113983e-05 -6.119917e-04 1.787791e-05 -1.371802e-04 4.553918e-06 -2.970648e-05 m - transition from old to new coordinates 20 -6.3192e-09 1.6341e-07 -4.7326e-09 1.1188e-06 -5.7442e-09 7.392e-06 -3.5816e-07 4.2371e-05 -3.0849e-07 0.00019906 2.9557e-05 0.00088805 -0.00010187 0.0041854 -0.00014589 0.009907 0.005118 0.019926 -0.032034 -1.0021 -8.9215e-08 7.9897e-09 -1.0817e-06 -2.6495e-08 -7.6657e-06 1.2341e-07 -4.6118e-05 -1.2919e-06 -0.00022215 -4.1724e-05 -0.0010035 7.6087e-05 -0.0047439 -1.4895e-05 -0.011202 -0.006256 -0.02256 0.034534 1.0041 0.029363 -5.078e-10 8.9905e-07 3.6589e-08 7.7839e-06 1.1304e-08 4.9844e-05 2.2549e-06 0.00024791 5.1485e-05 0.0011361 -6.8513e-05 0.005401 8.2451e-05 0.012648 0.0072781 0.025046 -0.038961 -1.0057 -0.033222 0.017556 6.6258e-07 5.8989e-08 7.4605e-06 1.7837e-07 5.3329e-05 3.4956e-06 0.00027767 6.3793e-05 0.0012992 -5.6225e-05 0.0062316 0.0001607 0.014559 0.0084911 0.02845 -0.044318 -1.0073 -0.036944 0.019395 0.0049913 -5.9401e-08 -6.701e-06 -3.7128e-07 -5.5768e-05 -5.086e-06 -0.00031076 -8.005e-05 -0.001496 3.2595e-05 -0.0072631 -0.0002904 -0.016916 -0.010116 -0.032444 0.050536 1.0096 0.041526 -0.021878 -0.0056268 -0.0077831 5.1412e-06 5.6139e-07 5.6181e-05 7.1472e-06 0.00034569 0.00010179 0.0017354 9.0848e-06 0.008575 0.00049236 0.019943 0.012262 0.03756 -0.058259 -1.0127 -0.047167 0.02461 0.0065396 0.0086795 0.00019799 6.9664e-07 5.2974e-05 9.5552e-06 0.00037972 0.00013078 0.0020264 8.0442e-05 0.010272 0.00081249 0.023881 0.015181 0.043998 -0.067949 -1.0171 -0.054118 0.028 0.0077289 0.0097972 0.00026738 0.0028052 -4.3167e-05 -1.2013e-05 -0.0004063 -0.00016899 -0.0023789 -0.00020281 -0.012521 -0.0013344 -0.029174 -0.019297 -0.052357 0.080437 1.0236 0.062784 -0.032048 -0.0092708 -0.011106 -0.00040224 -0.003091 -4.4633e-05 1.273e-05 0.00041442 0.0002174 0.0027986 0.00041472 0.015595 0.0022196 0.036551 0.025363 0.063492 -0.096983 -1.0338 -0.073877 0.037108 0.011363 0.012735 0.00060425 0.0034274 7.5286e-05 0.00043157 0.00037738 0.00027071 0.0032819 0.00078994 0.01996 0.0038023 0.047374 0.034834 0.078922 -0.11979 -1.0504 -0.08852 0.043567 0.014326 0.014801 0.00091035 0.0038168 0.00012529 0.00044642 3.6134e-05 0.00030462 0.0038127 0.0014754 0.026522 0.0068529 0.064459 0.050833 0.10152 -0.15304 -1.0792 -0.10875 0.052158 0.018756 0.01756 0.0013969 0.0042877 0.00019977 0.00045417 4.1298e-05 4.3387e-05 0.0041372 0.0028185 0.037367 0.013447 0.094734 0.081185 0.13763 -0.20598 -1.1343 -0.13881 0.064349 0.02595 0.021539 0.0022239 0.0048927 0.0003146 0.00044784 4.5586e-05 2.9565e-05 5.5278e-07 0.005849 0.058624 0.030996 0.16079 0.15106 0.20522 -0.30437 -1.2574 -0.18989 0.083952 0.039359 0.028197 0.0038086 0.0058012 0.00050588 0.00041916 4.3668e-05 4.8376e-06 -3.6192e-06 -9.8492e-06 0.11724 0.10777 0.39086 0.39669 0.39141 -0.56345 -1.6428 -0.31115 0.12642 0.073219 0.043963 0.0079016 0.0078778 0.00091808 0.00036192 1.6334e-05 -4.6919e-05 -1.7979e-05 -2.3565e-05 -5.2062e-06 -0.52592 -0.97882 0.39989 0.97223 -0.739 -0.53076 0.011011 0.051176 0.046684 0.0061091 0.0047859 0.0015699 -0.00017365 4.5216e-05 -0.00014106 -9.5326e-06 -3.2136e-05 -5.1983e-06 -5.0016e-06 -1.1235e-06 0.40792 -0.42831 -1.1571 0.99034 1.1174 -0.078426 -0.16891 -0.09771 -0.022732 -0.0014384 -0.0032295 0.0017185 0.00032022 0.00041507 0.00010945 5.8144e-05 2.4952e-05 5.3904e-06 3.6876e-06 2.1203e-07 2.5946 4.9475 4.6125 3.081 -0.78735 -2.2937 -1.0159 -0.15922 0.072215 0.057177 0.026556 0.014715 0.0046537 0.0016251 0.00034044 8.0679e-05 -1.0235e-05 -1.9594e-05 -1.1318e-05 -7.053e-06 1.0964 3.1561 2.7816 1.2401 -3.3565 -5.2111 -1.0788 0.49398 0.3621 0.17095 0.041881 0.02426 0.0030486 4.1161e-05 -0.00045686 -0.0004103 -0.00017169 -0.00011878 -3.5825e-05 -2.2031e-05 -3.0209 -2.6711 -1.6545 -0.67838 0.47401 1.1083 0.51647 0.029868 -0.050751 -0.037019 -0.014156 -0.0069927 -0.0023611 -0.00054747 -0.00013815 1.233e-05 1.3009e-05 1.7415e-05 7.14e-06 4.3628e-06 -0.072512 -0.06078 1.567 2.8359 2.7791 0.34899 -0.78727 -0.41672 -0.13372 -0.018239 -0.0010155 0.0030266 0.0037078 0.0014171 0.00075274 0.00024468 0.00011566 3.2824e-05 1.2311e-05 3.1842e-06 mInv - transition from new to old coordinates 20 5.5453e-09 1.4306e-07 4.8524e-08 -1.0109e-06 -3.6023e-07 -7.3917e-06 3.3635e-06 5.6907e-05 3.0708e-05 -0.00044282 0.00029321 -0.0039737 0.0055101 -0.050899 0.26273 -0.054651 -0.2761 -0.027501 -0.63554 0.095804 -1.8112e-07 -5.7007e-08 -1.2556e-06 4.013e-07 8.7745e-06 3.6058e-06 -6.3392e-05 -2.8181e-05 -0.00044382 0.00021664 -0.0034818 0.0036823 -0.032256 0.048957 -0.44756 0.35497 0.46799 -0.08644 0.50608 -0.32512 5.0732e-08 1.3357e-06 3.9213e-07 -9.0594e-06 -3.3682e-06 -6.228e-05 2.3884e-05 0.0004039 0.00014757 -0.0028361 0.002409 -0.022305 0.021015 -0.12963 0.077516 -0.71609 -0.28012 0.098808 -0.33009 0.42269 -1.3545e-06 -3.6764e-07 -8.8497e-06 3.0101e-06 5.8548e-05 1.9785e-05 -0.00035986 -0.0001031 -0.0023458 0.0016663 -0.016717 0.011393 -0.074871 0.064794 0.43711 0.53975 0.41379 -0.20247 0.28787 -0.2826 2.7769e-07 8.3414e-06 2.6536e-06 -5.3658e-05 -1.6267e-05 -0.00031707 7.2912e-05 0.0019615 0.0012071 -0.013149 0.007011 -0.052141 0.020408 -0.24163 -0.56931 -0.17252 -0.3663 0.24756 -0.17124 0.537 -7.7585e-06 -2.3163e-06 -4.8601e-05 1.3386e-05 0.00027813 5.2096e-05 -0.0016547 -0.00090412 -0.010638 0.0046624 -0.039388 0.0051275 -0.16385 0.311 0.33195 0.091081 0.47342 -0.45942 0.21672 -0.44106 1.7111e-06 4.3519e-05 1.1143e-05 -0.00024391 -3.758e-05 -0.0014086 0.00069634 0.0087837 0.0032691 -0.031072 -0.00096234 -0.11959 0.23171 -0.84988 -0.15261 -0.11582 -0.24143 0.21068 -0.16061 0.33084 -3.9141e-05 -9.3361e-06 -0.00021471 2.7302e-05 0.0012102 0.0005494 -0.0073723 -0.0023875 -0.025225 -0.0034844 -0.09144 0.17674 -0.92495 0.25931 0.070793 0.10101 0.17204 -0.13311 0.11275 -0.14506 6.4252e-06 0.00018872 2.0314e-05 -0.0010484 -0.00044253 -0.0062741 0.0018022 0.020922 -0.0044584 -0.072322 0.13867 -0.95764 0.20032 -0.1584 -0.053052 -0.061576 -0.069267 0.044024 -0.051995 0.097325 -0.00016786 -1.5191e-05 -0.00091669 0.00036292 0.0054037 0.0013983 -0.017651 0.004723 -0.058719 0.11159 -0.97416 0.156 -0.11927 0.031148 0.035347 0.032614 0.055246 -0.042382 0.032539 -0.046406 5.2458e-06 0.00080314 0.0003037 -0.0046997 -0.00111 -0.015101 -0.0046572 0.048682 0.091733 -0.9833 0.12424 -0.09197 0.011817 -0.051182 -0.022826 -0.015821 -0.024308 0.017896 -0.015565 0.034161 -0.00071415 -0.00025832 -0.0041274 0.00089885 0.013074 -0.004442 -0.041054 -0.076772 -0.9887 0.10114 -0.072888 0.0031546 -0.03964 0.016436 0.011518 0.0084788 0.018495 -0.015408 0.01039 -0.016217 0.00019568 0.0036354 0.00074473 -0.011419 0.004167 -0.035103 0.065219 0.99206 0.083916 -0.059175 -0.00083059 -0.031424 0.0098 -0.01891 -0.0060659 -0.0046785 -0.0075336 0.0057666 -0.0049826 0.010415 -0.0032413 -0.00062393 -0.010075 -0.0038802 0.030385 0.056116 -0.99426 -0.070766 -0.049023 -0.0026603 -0.025507 0.0062064 -0.014778 0.0052594 0.0028875 0.0026341 0.0051135 -0.0041401 0.0030306 -0.00444 0.00041297 0.008861 -0.0035683 -0.026475 -0.048793 -0.99574 0.060518 0.041326 -0.0034491 -0.021133 0.0041608 -0.011713 0.0031595 -0.0047354 -0.0015933 -0.0013632 -0.0019644 0.0014297 -0.0013384 0.0027162 -0.0079377 0.0033002 -0.02337 0.042848 0.99677 0.052351 -0.035317 0.0037209 -0.017802 0.0029256 -0.0094879 0.0020203 -0.0035124 0.001176 0.00078928 0.00069722 0.0013234 -0.00106 0.0007772 -0.0011474 -0.0033629 0.020479 0.038041 -0.99755 -0.045786 -0.030648 -0.0037247 0.015229 0.002141 -0.0078473 0.0013716 -0.0026837 0.00063232 -0.001182 -0.00042778 -0.00033959 -0.00050929 0.0003762 -0.00033878 0.00070301 -0.018536 -0.03421 -0.99808 0.040207 0.026767 -0.0036335 -0.013165 -0.001613 -0.0065988 0.00097655 -0.0021141 0.00036218 -0.00085803 0.00031353 0.00020197 0.00017082 0.00033658 -0.00027284 0.00019593 -0.00029435 0.029741 0.99863 0.035615 -0.023791 0.0034368 -0.011558 0.0012584 0.0056441 0.00072617 -0.0017145 0.00022099 -0.00064548 0.00017331 -0.00030129 -0.00010458 -8.3669e-05 -0.00012736 9.4878e-05 -8.4806e-05 0.0001749 -0.99934 -0.032471 -0.021067 -0.0031216 0.010189 0.0010371 -0.0048787 -0.00056615 -0.0014186 0.00014377 -0.00050161 0.00010386 -0.0002163 7.8971e-05 4.8371e-05 4.21e-05 8.1722e-05 -6.5996e-05 4.7982e-05 -7.1688e-05 Log norm =-1.43933e-01 for coord=15 l_i :-6.60982e+03 -5.35848e+03 -4.30560e+03 -3.39492e+03 -2.65575e+03 -2.02151e+03 -1.52000e+03 -1.10621e+03 -7.84187e+02 -5.33505e+02 -3.46959e+02 -2.11061e+02 -1.16841e+02 -5.38215e+01 -1.43933e-01 -1.43933e-01 -6.83325e+00 -6.83325e+00 -4.20031e+00 -4.20031e+00 -7.91791e+03 -9.65070e+03 -1.16410e+04 -1.39115e+04 -1.64974e+04 -1.94156e+04 -2.26980e+04 -2.63702e+04 -3.04639e+04 -3.50092e+04 -4.00388e+04 -4.55853e+04 -5.16829e+04 -5.83665e+04 -6.56725e+04 -7.36381e+04 -8.23016e+04 -9.17025e+04 -1.01881e+05 -1.12879e+05 -1.24740e+05 diff. estm L2=8.66498e-03 H1=3.84126e-02 C0=1.40082e-02 C1=6.50912e-02 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[-4.14668e-04,-3.85036e-04] +[-6.79759e+03,-6.79727e+03]x_{1} \\ x'_{2}&=&[4.05171e-05,6.14187e-05] +[-5.50209e+03,-5.50182e+03]x_{2} \\ x'_{3}&=&[-2.62042e-04,-2.07934e-04] +[-4.39932e+03,-4.39911e+03]x_{3} \\ x'_{4}&=&[2.23866e-05,5.35681e-05] +[-3.46882e+03,-3.46865e+03]x_{4} \\ x'_{5}&=&[4.85464e-05,1.76290e-04] +[-2.69273e+03,-2.69260e+03]x_{5} \\ x'_{6}&=&[-1.38766e-05,4.67594e-05] +[-2.05266e+03,-2.05256e+03]x_{6} \\ x'_{7}&=&[-1.74654e-04,1.34257e-04] +[-1.53224e+03,-1.53216e+03]x_{7} \\ x'_{8}&=&[-7.06199e-05,7.10760e-05] +[-1.11566e+03,-1.11560e+03]x_{8} \\ x'_{9}&=&[-3.43776e-04,3.42989e-04] +[-7.88407e+02,-7.88364e+02]x_{9} \\ x'_{10}&=&[-1.52697e-04,1.47344e-04] +[-5.36957e+02,-5.36925e+02]x_{10} \\ x'_{11}&=&[-6.31585e-04,6.37449e-04] +[-3.48865e+02,-3.48843e+02]x_{11} \\ x'_{12}&=&[-3.21015e-04,3.16738e-04] +[-2.12733e+02,-2.12717e+02]x_{12} \\ x'_{13}&=&[-1.09392e-03,1.09676e-03] +[-1.18152e+02,-1.18142e+02]x_{13} \\ x'_{14}&=&[-9.18346e-04,9.17434e-04] +[-5.54043e+01,-5.53959e+01]x_{14} \\ x'_{15}&=&[-7.51828e-04,7.50841e-04] +[-1.28222e+00,-1.28092e+00]x_{15} +[1.54791e+01,1.54798e+01]x_{16} \\ x'_{16}&=&[-4.82726e-04,4.82220e-04] +[-1.54801e+01,-1.54788e+01]x_{15} +[-1.28190e+00,-1.28103e+00]x_{16} \\ x'_{17}&=&[-3.00722e-03,3.00901e-03] +[-1.24015e+01,-1.23959e+01]x_{17} +[6.90537e+00,6.91007e+00]x_{18} \\ x'_{18}&=&[-4.98034e-03,4.98286e-03] +[-6.91320e+00,-6.90232e+00]x_{17} +[-1.24032e+01,-1.23938e+01]x_{18} \\ x'_{19}&=&[-1.20476e-03,1.20692e-03] +[-6.77117e+00,-6.76971e+00]x_{19} +[6.16779e+00,6.17059e+00]x_{20} \\ x'_{20}&=&[-1.46589e-03,1.46493e-03] +[-6.17038e+00,-6.16799e+00]x_{19} +[-6.77280e+00,-6.76808e+00]x_{20} \\ \end{eqnarray*} **************************** a fixed point from giant branch nu= 0.04+[-1e-07,1e-07] alpha=[99.9998,100] dimensions m= 21 M=42 delta=0.00025 number of iterates=8 starting point : 1.1262 -1.15624 -0.363754 -1.02332 -0.00640163 -0.666316 0.0490264 -0.20299 -0.00241362 -0.0580098 0.000757805 -0.0171936 0.000620093 -0.00447838 0.000117739 -0.00110122 3.16032e-05 -0.00026972 9.60494e-06 -6.41321e-05 2.50031e-06 fixed point : 1.1262 -1.15624 -0.363754 -1.02332 -0.00640164 -0.666316 0.0490264 -0.20299 -0.00241362 -0.0580098 0.000757805 -0.0171936 0.000620093 -0.00447832 0.000117726 -0.00110108 3.15981e-05 -0.000269556 9.64226e-06 -6.39913e-05 2.4066e-06 difference fixed - starting : -8.67194e-10 6.28196e-10 -1.77957e-09 6.30115e-10 -3.04548e-09 3.12124e-09 -6.82228e-09 -2.85878e-09 -6.60166e-10 3.0512e-09 -4.82608e-10 2.01825e-08 1.56993e-10 5.83224e-08 -1.29816e-08 1.4029e-07 -5.14862e-09 1.64527e-07 3.73204e-08 1.408e-07 -9.37099e-08 Isolating neighborhood (the set N):[9.014606e-08,9.053874e-08] [1.339911e-07,1.348515e-07] [-5.103962e-08,-5.051242e-08] [1.591832e-07,1.616202e-07] [8.524385e-09,9.620629e-09] [1.291068e-07,1.378229e-07] [-4.303451e-09,-2.218799e-10] [3.388697e-08,6.888810e-08] [-4.260030e-09,1.541875e-08] [-5.533741e-08,8.736881e-08] [-4.590028e-08,4.249991e-08] [-2.893873e-07,2.884347e-07] [-2.769073e-07,2.752867e-07] [-1.631236e-06,1.613440e-06] [-4.432227e-06,4.408462e-06] [-1.736631e-04,1.736631e-04] [-1.736629e-04,1.736629e-04] [-4.587847e-05,4.587847e-05] [-4.587875e-05,4.587875e-05] [-3.685510e-05,3.685510e-05] [-3.685510e-05,3.685510e-05] W=1.126204e+00+[-1.000950e-04,1.000950e-04] -1.156238e+00+[-1.830013e-04,1.830013e-04] -3.637545e-01+[-1.702023e-04,1.702023e-04] -1.023325e+00+[-2.197019e-04,2.197019e-04] -6.401637e-03+[-1.678950e-04,1.678950e-04] -6.663156e-01+[-1.399548e-04,1.399548e-04] 4.902641e-02+[-8.865854e-05,8.865854e-05] -2.029901e-01+[-6.201137e-05,6.201137e-05] -2.413625e-03+[-3.655719e-05,3.655719e-05] -5.800978e-02+[-2.365819e-05,2.365819e-05] 7.578050e-04+[-1.314438e-05,1.314438e-05] -1.719361e-02+[-7.936574e-06,7.936574e-06] 6.200935e-04+[-4.191936e-06,4.191936e-06] -4.478324e-03+[-2.441475e-06,2.441475e-06] 1.177260e-04+[-1.246843e-06,1.246843e-06] -1.101082e-03+[-7.054029e-07,7.054029e-07] 3.159806e-05+[-3.512559e-07,3.512559e-07] -2.695559e-04+[-1.944366e-07,1.944366e-07] 9.642262e-06+[-9.488986e-08,9.488986e-08] -6.399127e-05+[-5.173622e-08,5.173622e-08] 2.406602e-06+[-2.501397e-08,2.501397e-08] ------------------------------------- Self-consistent bounds k=1 b=1.126204e+00+[-1.000950e-04,1.000950e-04] k=2 b=-1.156238e+00+[-1.830013e-04,1.830013e-04] k=3 b=-3.637545e-01+[-1.702023e-04,1.702023e-04] k=4 b=-1.023325e+00+[-2.197019e-04,2.197019e-04] k=5 b=-6.401637e-03+[-1.678950e-04,1.678950e-04] k=6 b=-6.663156e-01+[-1.399548e-04,1.399548e-04] k=7 b=4.902641e-02+[-8.865854e-05,8.865854e-05] k=8 b=-2.029901e-01+[-6.201137e-05,6.201137e-05] k=9 b=-2.413625e-03+[-3.655719e-05,3.655719e-05] k=10 b=-5.800978e-02+[-2.365819e-05,2.365819e-05] k=11 b=7.578050e-04+[-1.314438e-05,1.314438e-05] k=12 b=-1.719361e-02+[-7.936574e-06,7.936574e-06] k=13 b=6.200935e-04+[-4.191936e-06,4.191936e-06] k=14 b=-4.478324e-03+[-2.441475e-06,2.441475e-06] k=15 b=1.177260e-04+[-1.246843e-06,1.246843e-06] k=16 b=-1.101082e-03+[-7.054029e-07,7.054029e-07] k=17 b=3.159806e-05+[-3.512559e-07,3.512559e-07] k=18 b=-2.695559e-04+[-1.944366e-07,1.944366e-07] k=19 b=9.642262e-06+[-9.488986e-08,9.488986e-08] k=20 b=-6.399127e-05+[-5.173622e-08,5.173622e-08] k=21 b=2.406602e-06+[-2.501397e-08,2.501397e-08] k=22 b=-1.479548e-05+[-1.387685e-08,1.387685e-08] k=23 b=5.939099e-07+[-6.556707e-09,6.556707e-09] k=24 b=-3.378472e-06+[-3.449502e-09,3.449502e-09] k=25 b=1.486561e-07+[-1.618107e-09,1.618107e-09] k=26 b=-7.609938e-07+[-8.446387e-10,8.446387e-10] k=27 b=3.587942e-08+[-3.999542e-10,3.999542e-10] k=28 b=-1.691467e-07+[-2.096446e-10,2.096446e-10] k=29 b=8.485258e-09+[-1.195323e-10,1.195323e-10] k=30 b=-3.722991e-08+[-6.965913e-11,6.965913e-11] k=31 b=1.989581e-09+[-1.004576e-10,1.004576e-10] k=32 b=-8.124085e-09+[-7.143965e-11,7.143965e-11] k=33 b=4.602188e-10+[-2.193403e-10,2.193403e-10] k=34 b=-1.758590e-09+[-1.671821e-10,1.671821e-10] k=35 b=1.051591e-10+[-6.111934e-10,6.111934e-10] k=36 b=-3.780600e-10+[-5.582847e-10,5.582847e-10] k=37 b=2.381089e-11+[-1.756324e-09,1.756324e-09] k=38 b=-8.078287e-11+[-1.308059e-09,1.308059e-09] k=39 b=5.344838e-12+[-2.727853e-09,2.727853e-09] k=40 b=-1.716664e-11+[-2.598882e-09,2.598882e-09] k=41 b=1.190010e-12+[-3.639101e-09,3.639101e-09] k=42 b=-3.630558e-12+[-4.250980e-09,4.250980e-09] Tail : 4.333513e+10/k^10 ------------------------------------- Galerkin errors (epsilons) k=1 -9.410310e-11+[-3.882951e-11,3.882951e-11] k=2 4.003992e-09+[-6.748984e-11,6.748984e-11] k=3 -1.149632e-09+[-8.535626e-11,8.535626e-11] k=4 3.377897e-08+[-1.355075e-10,1.355075e-10] k=5 -6.721944e-09+[-1.593334e-10,1.593334e-10] k=6 2.072802e-07+[-4.115765e-10,4.115765e-10] k=7 -3.573920e-08+[-4.881266e-10,4.881266e-10] k=8 1.124328e-06+[-1.772758e-09,1.772758e-09] k=9 -2.237727e-07+[-2.015084e-09,2.015084e-09] k=10 5.415814e-06+[-7.823737e-09,7.823737e-09] k=11 -5.350782e-07+[-7.709789e-09,7.709789e-09] k=12 2.209254e-05+[-3.032958e-08,3.032958e-08] k=13 -1.175557e-07+[-2.736843e-08,2.736843e-08] k=14 8.993342e-05+[-1.142150e-07,1.142150e-07] k=15 -2.543224e-05+[-1.083056e-07,1.083056e-07] k=16 3.398489e-04+[-4.059230e-07,4.059230e-07] k=17 -1.691083e-05+[-2.683816e-07,2.683816e-07] k=18 6.321627e-04+[-7.451576e-07,7.451576e-07] k=19 1.767756e-04+[-6.199359e-07,6.199359e-07] k=20 8.357130e-04+[-1.052349e-06,1.052349e-06] k=21 -6.846717e-04+[-1.210672e-06,1.210672e-06] ------------------------------------- Coordinate change: shift 1.126204e+00 -1.156238e+00 -3.637544e-01 -1.023324e+00 -6.401633e-03 -6.663155e-01 4.902641e-02 -2.029901e-01 -2.413624e-03 -5.800978e-02 7.578054e-04 -1.719363e-02 6.200933e-04 -4.478382e-03 1.177390e-04 -1.101222e-03 3.160320e-05 -2.697204e-04 9.604942e-06 -6.413206e-05 2.500311e-06 m - transition from old to new coordinates 21 1.1711e-07 -1.5321e-09 3.5829e-07 -4.3589e-09 2.3347e-06 -1.7729e-08 1.3385e-05 -7.3999e-07 6.6496e-05 3.0836e-06 0.00027643 4.1717e-05 0.001174 -0.00021699 0.0048629 0.00029994 0.010076 0.0050469 0.019098 -0.03588 -1.0024 -3.4705e-09 -3.8671e-07 -5.0423e-09 -2.3145e-06 -6.2844e-08 -1.4131e-05 2.6656e-07 -7.2735e-05 -6.2836e-06 -0.00030824 -5.9804e-05 -0.0013213 0.00018863 -0.0054759 -0.00056898 -0.011343 -0.0061953 -0.021521 0.038522 1.0049 0.032742 2.0594e-07 1.365e-08 2.2761e-06 1.0682e-07 1.4701e-05 -1.8863e-08 7.923e-05 8.3542e-06 0.00034366 7.378e-05 0.0014887 -0.00018989 0.0061901 0.00073181 0.012706 0.0071624 0.02372 -0.043107 -1.0066 -0.037561 0.016911 -9.5648e-09 -1.8774e-06 -1.598e-07 -1.5e-05 -2.967e-07 -8.5981e-05 -1.0831e-05 -0.00038543 -9.0914e-05 -0.0016947 0.00019067 -0.0070913 -0.0009092 -0.014514 -0.0082733 -0.026717 0.048719 1.0083 0.041042 -0.018496 -0.0050164 -1.4033e-06 -1.7873e-07 -1.4445e-05 -6.8091e-07 -9.2444e-05 -1.405e-05 -0.00043313 -0.00011387 -0.0019429 0.0001804 -0.0081972 -0.0011708 -0.016706 -0.0097723 -0.030148 0.055152 1.0107 0.045872 -0.020771 -0.0056117 -0.0080312 -1.8402e-07 -1.3074e-05 -1.1122e-06 -9.7033e-05 -1.8182e-05 -0.00048669 -0.00014472 -0.0022457 0.00015425 -0.0095901 -0.001538 -0.01949 -0.011714 -0.034525 0.063049 1.0139 0.05172 -0.023191 -0.0064921 -0.008913 -0.00061583 -1.0153e-05 -1.5656e-06 -9.8545e-05 -2.3186e-05 -0.00054431 -0.0001863 -0.0026173 0.00010127 -0.011369 -0.0020684 -0.023051 -0.014309 -0.039915 0.072783 1.0184 0.058864 -0.02618 -0.0076201 -0.010019 -0.00073507 -0.0033593 -1.844e-06 -9.4125e-05 -2.8899e-05 -0.0006025 -0.00024279 -0.0030755 1.1941e-06 -0.013699 -0.0028596 -0.027746 -0.017885 -0.046777 0.085124 1.0248 0.067662 -0.029666 -0.0090564 -0.011299 -0.00093879 -0.0037008 -4.2394e-06 -7.8308e-05 -3.427e-05 -0.00065261 -0.00031922 -0.003643 -0.00018241 -0.016834 -0.0040878 -0.034128 -0.022999 -0.055669 0.10114 1.0345 0.078748 -0.033955 -0.010973 -0.012883 -0.0012265 -0.0041064 -3.6441e-05 -0.00062073 -3.4548e-05 -0.00068027 -0.00042 -0.0043436 -0.00051975 -0.021213 -0.0060929 -0.043191 -0.030676 -0.067572 0.12262 1.0496 0.093087 -0.039297 -0.013622 -0.014868 -0.0016375 -0.0045803 -9.2503e-05 -0.00065434 -5.82e-05 0.00063784 0.00054 0.0052058 0.0011537 0.027646 0.0095924 0.056857 0.04296 0.0842 -0.15278 -1.0746 -0.11236 0.046184 0.017453 0.017473 0.0022524 0.0051598 0.00017711 0.00068614 6.8899e-05 8.2571e-05 0.00065183 0.0062693 0.0024 0.037855 0.016302 0.07938 0.064448 0.10896 -0.1981 -1.1187 -0.13979 0.055496 0.02337 0.021107 0.0032285 0.005903 0.00030835 0.00071118 8.1995e-05 7.1955e-05 5.1139e-06 -0.0071722 -0.0051853 -0.056355 -0.031187 -0.12228 -0.10753 -0.14991 0.27405 1.206 0.18265 -0.069201 -0.033459 -0.02674 -0.0049261 -0.0069614 -0.00052382 -0.00072735 -9.5147e-05 -5.2425e-05 -2.1965e-06 4.969e-06 -0.012531 -0.099201 -0.0748 -0.22941 -0.2176 -0.23318 0.42995 1.4139 0.26323 -0.093062 -0.054004 -0.037414 -0.0084369 -0.0088382 -0.00092678 -0.00073846 -0.00010215 -1.5146e-05 7.6385e-06 1.8017e-05 4.5175e-06 -0.28542 -0.33992 -0.76543 -0.74767 -0.54574 0.96865 2.235 0.52113 -0.15678 -0.12004 -0.071371 -0.020268 -0.014876 -0.0021538 -0.00085785 -8.1268e-05 7.8183e-05 4.8027e-05 5.2613e-05 1.5523e-05 1.3734e-05 -0.26291 0.63253 1.1939 -0.99689 -1.1234 0.18728 0.21757 0.093955 0.01706 -0.00017746 0.0032373 -0.0032775 -0.00051829 -0.00060091 -0.00015019 -8.5705e-05 -3.543e-05 -5.0826e-06 -5.8038e-06 5.1584e-07 -6.6513e-07 -0.46206 -0.8282 0.50631 0.97867 -0.97524 -0.76515 -0.0043912 0.090648 0.0732 0.01588 0.010175 0.0030835 -0.00028707 8.3316e-06 -0.00027991 -4.9672e-05 -7.6684e-05 -1.734e-05 -1.3331e-05 -3.879e-06 -2.0255e-06 2.7165 4.3648 2.8691 0.94521 -1.2599 -0.91746 -0.34731 -0.15408 0.021506 0.021796 0.022229 0.0092217 0.003334 0.0016154 0.00023605 0.00015716 -2.3715e-05 5.3814e-07 -1.35e-05 -4.5383e-06 -3.5205e-06 -0.52892 1.108 1.1378 -0.22361 -3.2559 -3.9471 -0.65581 0.5611 0.37903 0.17071 0.04898 0.023229 0.0011958 -0.00092719 -0.00096735 -0.00067558 -0.00031031 -0.00018295 -6.1713e-05 -3.4897e-05 -1.0536e-05 -1.9875 -1.3656 0.10863 1.2392 1.873 1.1585 0.0080203 -0.27057 -0.15834 -0.060525 -0.018437 -0.0054053 0.00050172 0.00081966 0.00057348 0.00030834 0.00015044 6.9456e-05 2.7211e-05 1.1967e-05 4.1267e-06 1.5857 1.8609 3.0279 3.3291 2.3821 -0.49388 -1.4548 -0.60009 -0.1301 0.01043 0.018819 0.014806 0.0098426 0.0032806 0.0015579 0.00046902 0.00019567 4.0517e-05 1.0984e-05 -6.2038e-07 -2.295e-06 mInv - transition from new to old coordinates 21 -4.7206e-08 -1.7964e-08 -3.2571e-07 -1.1637e-07 2.1014e-06 -8.5087e-07 1.4241e-05 -7.4413e-06 9.9913e-05 -5.902e-05 -0.00071276 0.00057936 0.0061669 -0.010384 0.080338 0.070398 0.2087 -0.22544 -0.18042 -0.62411 0.26132 1.8322e-08 4.0449e-07 1.3572e-07 2.5854e-06 -9.4903e-07 1.6776e-05 -7.8371e-06 0.00010969 -5.1581e-05 0.00070436 0.00043857 -0.0053358 -0.0066771 0.045238 -0.084508 -0.35342 -0.36795 0.47359 0.10922 0.50131 -0.32726 -4.5376e-07 -1.3898e-07 -2.7373e-06 -9.1535e-07 1.7182e-05 -7.2573e-06 0.00010655 -4.1863e-05 0.00062982 -0.00029774 -0.004272 0.004335 0.030033 -0.031465 0.17133 0.68734 0.044886 -0.34769 0.01677 -0.26451 0.42748 1.1103e-07 2.749e-06 8.4912e-07 1.6681e-05 -6.4441e-06 9.9553e-05 -3.3639e-05 0.00055606 -0.00020825 0.0034922 0.0029827 -0.022049 -0.015772 0.090314 -0.11074 -0.50737 0.4867 0.40911 -0.11121 0.34618 -0.26566 -2.6725e-06 -7.777e-07 -1.5781e-05 -5.6171e-06 9.1008e-05 -2.6957e-05 0.00048773 -0.00014846 0.0029035 -0.0021627 -0.01718 0.0090811 0.0609 -0.038838 0.28076 0.084421 -0.60494 -0.37983 0.18584 -0.13326 0.4339 5.6423e-07 1.4567e-05 4.8844e-06 8.2241e-05 -2.1668e-05 0.00042674 -0.00010734 0.0024421 -0.001626 0.013842 0.0056879 -0.045421 -0.01413 0.18781 -0.36682 0.03382 0.39622 0.41692 -0.38929 0.28771 -0.42701 -1.3404e-05 -4.2725e-06 -7.3974e-05 -1.7529e-05 0.00037397 -7.8617e-05 0.0020753 -0.0012581 0.011405 -0.0037608 -0.035629 0.0038834 0.13569 -0.28349 0.77589 0.048102 -0.19822 -0.2606 0.20518 -0.17638 0.38206 3.0971e-06 6.606e-05 1.4402e-05 0.00032855 -5.8279e-05 0.001781 -0.00099746 0.0095607 -0.0025879 0.028836 -0.00072982 -0.10287 -0.21894 0.88922 -0.30183 -0.078831 0.10532 0.18968 -0.11884 0.16699 -0.18592 -5.9452e-05 -1.2063e-05 -0.00029029 -4.3608e-05 0.0015428 -0.00080749 0.0081305 -0.0018383 0.023871 0.0028436 -0.080781 0.1726 0.9375 -0.24416 0.17682 0.058856 -0.069365 -0.093095 0.040429 -0.061339 0.11974 7.4717e-06 0.00025614 3.3399e-05 0.0013469 -0.00066551 0.0069986 -0.0013405 0.020114 0.0037644 0.065199 0.13912 -0.96197 -0.19289 0.1346 -0.049786 -0.031434 0.049927 0.06474 -0.038017 0.052241 -0.057205 -0.0002291 -2.6399e-05 -0.0011864 -0.00055715 0.0060883 -0.00099907 0.017193 0.0040923 0.053792 -0.11441 -0.97549 0.15445 0.10348 -0.022153 0.057946 0.014454 -0.032506 -0.032705 0.017812 -0.018875 0.042288 1.0557e-05 0.0010465 0.00047429 0.0053411 -0.00075844 0.014871 0.0041206 0.045181 -0.095724 0.98347 0.12598 -0.081571 -0.0089736 0.045127 -0.022771 -0.0067164 0.018737 0.022892 -0.015994 0.017823 -0.02165 -0.00093665 -0.00041176 -0.0047272 -0.0005853 0.012997 0.0039993 0.038517 -0.081286 0.98843 -0.10458 -0.065861 0.0025521 0.035786 -0.013423 0.023368 0.0039517 -0.0099284 -0.011119 0.0068518 -0.0068373 0.014861 0.00031779 0.00419 0.0004632 0.011442 0.0038069 0.03323 -0.069898 0.99165 -0.088187 0.054299 -0.00063921 -0.02904 -0.008209 0.01875 -0.0084546 -0.0024294 0.0052026 0.0071328 -0.0048307 0.0057832 -0.0068701 -0.0037569 -0.00037134 -0.010169 0.0035929 0.028992 -0.060765 0.99381 -0.075374 0.045558 0.0022211 -0.024042 0.0052622 0.014989 -0.0053079 0.0066756 0.0014466 -0.0027672 -0.0032513 0.0018183 -0.0020549 0.004278 0.0001413 0.0089874 -0.0033362 0.025412 -0.053312 0.99532 -0.0652 0.038825 0.0029698 0.02025 0.003519 -0.012193 -0.003464 0.0050767 -0.002123 -0.00076729 0.001505 0.0020132 -0.0013056 0.0016214 -0.0018946 -0.008115 0.0030932 -0.022567 -0.047199 0.99639 -0.056934 0.033479 0.0032796 0.017294 -0.0024381 -0.010099 0.0023814 0.0039057 -0.0011841 0.0017703 0.00039542 -0.00080806 -0.00090504 0.00050795 -0.0005587 0.0011817 -0.0032568 0.019857 0.042165 0.99722 -0.050199 0.029298 0.0033395 0.014971 -0.0017425 0.0085097 0.0017161 -0.0030891 -0.00069165 0.0013056 -0.00058889 -0.00019624 0.00042673 0.00055514 -0.00036893 0.00044204 -0.00052637 -0.018128 -0.038582 -0.99779 -0.044399 0.025762 0.0033185 0.013069 -0.001268 0.0072661 -0.0012831 -0.0025028 0.00042509 0.00098256 -0.00032895 0.00049169 0.00010177 -0.00021894 -0.00024661 0.0001426 -0.00015295 0.00032316 0.033134 0.99834 0.039641 0.023031 0.0031773 0.011577 -0.00095776 0.0062966 -0.00099459 0.0020765 0.00027517 -0.00076534 -0.00019428 0.00036037 -0.00016352 -5.2164e-05 0.0001118 0.0001479 -9.8472e-05 0.00011825 -0.00014134 -0.99924 -0.036339 -0.0205 0.002898 0.010281 -0.00077514 0.005504 -0.00080217 0.0017503 -0.00018815 -0.0006122 0.00012287 0.00026871 -9.3068e-05 0.00012892 2.7402e-05 -5.6609e-05 -6.4739e-05 3.7055e-05 -4.0616e-05 8.4492e-05 Log norm =-4.41403e-01 for coord=16 l_i :-7.13048e+03 -5.84311e+03 -4.74554e+03 -3.79012e+03 -3.00666e+03 -2.32573e+03 -1.78327e+03 -1.32790e+03 -9.67650e+02 -6.80560e+02 -4.61711e+02 -2.97137e+02 -1.78763e+02 -9.63485e+01 -4.11300e+01 -4.41403e-01 -4.41403e-01 -8.91248e+00 -8.91248e+00 -6.62727e+00 -6.62727e+00 -8.45725e+03 -1.02218e+04 -1.22355e+04 -1.45202e+04 -1.71098e+04 -2.00177e+04 -2.32759e+04 -2.69059e+04 -3.09379e+04 -3.53989e+04 -4.03197e+04 -4.57298e+04 -5.16608e+04 -5.81447e+04 -6.52146e+04 -7.29047e+04 -8.12500e+04 -9.02865e+04 -1.00051e+05 -1.10582e+05 -1.21918e+05 -1.34098e+05 diff. estm L2=1.51496e-03 H1=6.68738e-03 C0=2.50929e-03 C1=1.32251e-02 Basic Differential Inclusion in block coordinates \begin{eqnarray*} x'_{1}&=&[6.61248e-04,6.64124e-04] +[-7.33529e+03,-7.33525e+03]x_{1} \\ x'_{2}&=&[8.03743e-04,8.08899e-04] +[-5.99848e+03,-5.99845e+03]x_{2} \\ x'_{3}&=&[-2.47596e-04,-2.45040e-04] +[-4.85108e+03,-4.85105e+03]x_{3} \\ x'_{4}&=&[6.16718e-04,6.26156e-04] +[-3.87427e+03,-3.87425e+03]x_{4} \\ x'_{5}&=&[2.60109e-05,2.93557e-05] +[-3.05135e+03,-3.05133e+03]x_{5} \\ x'_{6}&=&[3.05322e-04,3.25933e-04] +[-2.36488e+03,-2.36487e+03]x_{6} \\ x'_{7}&=&[-7.74387e-06,-3.99265e-07] +[-1.79947e+03,-1.79946e+03]x_{7} \\ x'_{8}&=&[4.54090e-05,9.23105e-05] +[-1.34001e+03,-1.34001e+03]x_{8} \\ x'_{9}&=&[-4.14372e-06,1.49978e-05] +[-9.72704e+02,-9.72698e+02]x_{9} \\ x'_{10}&=&[-3.78809e-05,5.98079e-05] +[-6.84549e+02,-6.84545e+02]x_{10} \\ x'_{11}&=&[-2.12763e-05,1.97001e-05] +[-4.63536e+02,-4.63533e+02]x_{11} \\ x'_{12}&=&[-8.64064e-05,8.61219e-05] +[-2.98586e+02,-2.98584e+02]x_{12} \\ x'_{13}&=&[-4.97136e-05,4.94226e-05] +[-1.79533e+02,-1.79531e+02]x_{13} \\ x'_{14}&=&[-1.58267e-04,1.56540e-04] +[-9.70237e+01,-9.70225e+01]x_{14} \\ x'_{15}&=&[-1.85455e-04,1.84461e-04] +[-4.18436e+01,-4.18425e+01]x_{15} \\ x'_{16}&=&[-5.84963e-05,5.84887e-05] +[-6.89818e-01,-6.89752e-01]x_{16} +[1.73099e+01,1.73100e+01]x_{17} \\ x'_{17}&=&[-1.04397e-04,1.04492e-04] +[-1.73099e+01,-1.73099e+01]x_{16} +[-6.89861e-01,-6.89666e-01]x_{17} \\ x'_{18}&=&[-1.40262e-04,1.40651e-04] +[-9.67170e+00,-9.67143e+00]x_{18} +[1.05488e+01,1.05490e+01]x_{19} \\ x'_{19}&=&[-4.19230e-04,4.20797e-04] +[-1.05494e+01,-1.05486e+01]x_{18} +[-9.67193e+00,-9.67129e+00]x_{19} \\ x'_{20}&=&[-1.63315e-04,1.62952e-04] +[-7.27436e+00,-7.27416e+00]x_{20} +[4.60162e+00,4.60195e+00]x_{21} \\ x'_{21}&=&[-2.12210e-04,2.12577e-04] +[-4.60197e+00,-4.60160e+00]x_{20} +[-7.27458e+00,-7.27394e+00]x_{21} \\ \end{eqnarray*}