Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL1_07_PQ.dat at {9.8817483271490040629854411278790101774226774803133e-1 ,0 ,1.2905155266141899466594705780827733803044348148477e-1 ,0 ,1.4857887018896643133050011501406532414084522212085e-2 ,0 }
Validate the existence of a branch of period-1 points:
proveBranchHaloOrbits(this->cr3bpFixPointsSolver.pm,this->cr3bpFixPointsSolver.pm,c,s,this->fp,0,4,2,3,5,&(this->Dfp)): true
############################

y0[i][3]=[-1.0793162422988438221782832205949190171138539695701e-45 ,1.0795145814282418160509235770789339618354908905991e-45 ]
D0[i][3][0]=[-4.1934155620323009894479878975506080228449182917643e2 ,-4.1934155620323009894479878975506080228449176379510e2 ]
D0[i][3][2]=[-5.0248556846771918410212999170685823172916223820386e-40 ,5.0248527359335799503897620723638920866381580004003e-40 ]
dy0=[-6.3000880723324123193557160890653156325254643156498e-43 ,6.3000900557236415568302260335921808209338653246889e-43 ]
Ddy=[-2.0970345226851614515196810418593605937751976017840e3 ,-2.0970345226851614515196810387464628387745736282440e3 ]
dy=[-3.0042843854880479974362635456146455612878539525586e-46 ,3.0042853312956671766514680577900825254157270933761e-46 ]
r[4]=[-1.0000000000000000000316901234324314520230954186913e-30 ,1.0000000000000000000316901234324314520230954186913e-30 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-6.4114257700103895789875956172181213480355347398995e-42 ,6.4114257800204587480016370913786083697658259988264e-42 ]
D0[i][3][0]=[-5.9327565366679048414710949069821792506966012192366 ,-5.9327565366679048414710949069821792496326510724114 ]
D0[i][3][2]=[-8.1662323486307396595310641407759512319856759430044e-36 ,8.1662323496102640439038440645577928788317252718321e-36 ]
dy0=[-6.4203237327655317530383964634436396418437805227158e-42 ,6.4203237427756009055811907603953682472826943728131e-42 ]
Ddy=[-4.1529123982294423271500200595538677027918344323903e1 ,-4.1529123982294423271500200394151233157703792509988e1 ]
dy=[-1.5459810169612006033884714741312087074656943322524e-43 ,1.5459810193715739011277879195483536957672324466396e-43 ]
r[4]=[-1.0000000000000000000316901234324314520230954186913e-30 ,1.0000000000000000000316901234324314520230954186913e-30 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-1.2610944344427327949305394484015382198624054436959e-36 ,1.2610944344287480140523608100740338359945847229433e-36 ]
D0[i][3][0]=[-4.1934155620323009894479878975506093451419988818376e2 ,-4.1934155620323009894479878975506067005478370409069e2 ]
D0[i][3][2]=[-2.8004440437700235195686587973702971720838919713789e-30 ,2.8004440437680860368949817313890914884901783124029e-30 ]
dy0=[-1.2610950633722237860208446348931813824530847405389e-36 ,1.2610950633582390049882858788218876072187429412152e-36 ]
Ddy=[2.1254300383561816250942269760082395039102902134410e4 ,2.1254300383561816250942271383349037311592819662959e4 ]
dy=[-5.9333642632320013933711394210784048161235870951008e-41 ,5.9333642632977988121531505037523740791606128427911e-41 ]
r[4]=[-1.0000000000000000000316901234324314520230954186913e-30 ,1.0000000000000000000316901234324314520230954186913e-30 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-2.8548522025438292194052011510508838347882365699227e-33 ,2.8548522025438290145554718911914286775503620361445e-33 ]
D0[i][3][0]=[-4.6055158622185488150083573971646255367959255902677e-28 ,4.6055158622185488959025135909312001121870192693149e-28 ]
D0[i][3][2]=[-1.4222403042152866785042097528671674388711358075887e-26 ,1.4222403042152866757061743420974969598763468614627e-26 ]
dy0=[-2.8548522025438292194052602125282387475278068146098e-33 ,2.8548522025438290145555287808035972890345219101579e-33 ]
Ddy=[3.3726824196601431345615986436630216018918346043014e2 ,3.3726824196601431345615986541614649664331791550645e2 ]
dy=[-8.4646339243275250618351415079518166983814411680640e-36 ,8.4646339243275256692143902555016741191718061501919e-36 ]
r[4]=[-1.0000000000000000000316901234324314520230954186913e-30 ,1.0000000000000000000316901234324314520230954186913e-30 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

Intersection of two enclosures of dy(x,z) along fixed point curve:
intersection(r[4],fp[4],fp[4]): true
############################

DBif[i][3][4]=[-2.0970345226851614515196810403029229110449301823887e3 ,-2.0970345226851614515196810403029005215048410476393e3 ]
D0[i][5][0]=[4.5787001479910729206484737234896384635785824111838 ,4.5787001479910729206484737234896384635802111259627 ]
D0[i][3][0]=[-4.1934155620323009894479878975506080228449182917643e2 ,-4.1934155620323009894479878975506080228449176379510e2 ]
DBif[i][5][0]=[4.5787001479910729206484737234890822824967920845082 ,4.5787001479910729206484737234901946446620014526383 ]
DBif[i][3][0]=[-4.1934155620323009894479878975506813780205892548052e2 ,-4.1934155620323009894479878975505346676692466749101e2 ]
D[k][3][4]=[-2.0970345226851614515196810405368373300768942112448e3 ,-2.0970345226851614515196810400689861024728770187832e3 ]
_H(5,0,0)=[1.6928655869273486531623201443594566546809966151424e3 ,1.6928655869273486580847381300829210491497973908698e3 ]
_H(5,0,2)=[4.2243284291056300392373384244705833574697102721234e2 ,4.2243284291056316025022553119038816652348748508016e2 ]
Dg!=0.: true
############################

Check principal period of new branch:
!intersection(-g/Dg,r[2],tmp): true
############################

DBif[i][3][4]=[-4.1529123982294423271500200494845759782616083215610e1 ,-4.1529123982294423271500200494844150403006053618282e1 ]
D0[i][5][0]=[5.8755089758411554498525648905313841983315515389221e1 ,5.8755089758411554498525648905313841986561456344303e1 ]
D0[i][3][0]=[-5.9327565366679048414710949069821792506966012192366 ,-5.9327565366679048414710949069821792496326510724114 ]
DBif[i][5][0]=[5.8755089758411554498525648905313125205433740974172e1 ,5.8755089758411554498525648905314558764443230759352e1 ]
DBif[i][3][0]=[-5.9327565366679048414710949069822703188933610776797 ,-5.9327565366679048414710949069820881814358912139683 ]
D[k][3][4]=[-4.1529123982294423271500200500474579538245237140618e1 ,-4.1529123982294423271500200489215330647376899693274e1 ]
_H(5,0,0)=[9.0578572020680160933413137317020112576797440110618e2 ,9.0578572020682266361123187798853667011188904798622e2 ]
_H(5,0,2)=[8.4923845765504943162353284872062014296311767584982e2 ,8.4923845765562994745637645324649182430638804253519e2 ]
Dg!=0.: true
############################

Check principal period of new branch:
!intersection(-g/Dg,r[2],tmp): true
############################

DBif[i][3][4]=[2.1254300383561816250942270571708870947450080567700e4 ,2.1254300383561816250942270571722561403245641229670e4 ]
D0[i][5][0]=[4.5787001479910729206484737234885912155077983798033 ,4.5787001479910729206484737234906857116509951408697 ]
D0[i][3][0]=[-4.1934155620323009894479878975506093451419988818376e2 ,-4.1934155620323009894479878975506067005478370409069e2 ]
DBif[i][5][0]=[4.5787001479910729206484737234881659340866811100521 ,4.5787001479910729206484737234911109930721124106209 ]
DBif[i][3][0]=[-4.1934155620323009894479878975506534002973604881819e2 ,-4.1934155620323009894479878975505626453924754345626e2 ]
D[k][3][4]=[2.1254300383561816250942270568589264988558587716507e4 ,2.1254300383561816250942270574842167362137134080863e4 ]
_H(5,0,0)=[-1.7850162418627971914048061641027064682870220792792e1 ,-1.7850143357256289928128170511418310584857764125090e1 ]
_H(5,0,2)=[-3.1300842318734694721932993339965463263249596727406e3 ,-3.1300834755964856627850061888015071493890748246662e3 ]
Dg!=0.: true
############################

Check principal period of new branch:
!intersection(-g/Dg,r[2],tmp): true
############################

DBif[i][3][4]=[3.3726824196601431345615986487792768998012885846216e2 ,3.3726824196601431345615986490452096685237251747443e2 ]
D0[i][5][0]=[-1.4023628452008239639567041115700965476362850642002e-27 ,1.4023628452008238608391206105812776974139312448176e-27 ]
D0[i][3][0]=[-4.6055158622185488150083573971646255367959255902677e-28 ,4.6055158622185488959025135909312001121870192693149e-28 ]
DBif[i][5][0]=[-1.4038388994562940885974648330546852731699947798160e-27 ,1.4038388994562939854798813320658664229476409604334e-27 ]
DBif[i][3][0]=[-4.6074983390654875104376196246616860116715477319516e-28 ,4.6074983390654875913317758184282605870626414109988e-28 ]
D[k][3][4]=[3.3726824196601431345615986483972243933385163895756e2 ,3.3726824196601431345615986494272621749864973697904e2 ]
_H(5,0,0)=[-2.4046154395617151495126225411077119704327782559569e-2 ,2.4046154395631318154829405880886491196861483664994e-2 ]
_H(5,0,2)=[-6.4644572988676604039596391845283057522934455457312e3 ,-6.4612294919703733477166544657571374330292737742513e3 ]
g=[-5.8417860496457440599929877561954470468703847879150e-27 ,5.8417860496457440348445691429115230038875545748807e-27 ]
Dg=[-6.4644572988676604039596391845283063187450152603608e3 ,-6.4612294919703733477166544657571368665777040596217e3 ]
r[2]=[-4.0000000000000000001267604937297258080923816747651e-30 ,4.0000000000000000001267604937297258080923816747651e-30 ]
Dg!=0.: true
############################

-g/Dg=[-9.0412916874498324667998429515205155442261083681768e-31 ,9.0412916874498324278778101642052480305274840028315e-31 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

Check intersection of two enclosures of hessian at bif point:intersection(H1,H[3],H[3]): true
############################

Check intersection of two enclosures of derivative at bif point:intersection(D1,D[3],D[3]): true
############################

T1={[-2.3556846570757356895082714372004847425648938679372e-29 ,2.3556846570757356479581391837189609640695956258360e-29 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-4.3627480744320290680046271644389223052650942148673e-30 ,4.3627480744320291509470901912374168023382834931168e-30 ],[0 ,0 ]}
DH[2]=[-3.7173008124307462371173347690519628790708426312604e-1 ,-3.7173008124307462371173347689115912946345034002337e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-3.7173008124307462371173347690538900325853575732541e-1 ,-3.7173008124307462371173347689096641411199884582767e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[3.3726824196601431345615986486929629989744346722575e2 ,3.3726824196601431345615986491315235693505790867369e2 ]
_H(5,0,0)=[-2.0283497846922092536406854401232982782965445081829e-6 ,2.0283497846922092497919890187364757276439022539452e-6 ]
_H(5,0,2)=[-6.4628433954947641822703157590449600528761793933514e3 ,-6.4628433953433193915750457079185689421191810671405e3 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-3.1384789335197239230767039895697167836931712628382e-10 ,3.1384789335197239171215907585111883021626507549910e-10 ],[0 ,0 ],[-5.7291747475421225451996227048066131246827630941235e-12 ,5.7291747475421225343287884360953800433705149181439e-12 ],[0 ,0 ]}
DH*T2=[-1.1691977731059219020065521817354672733215325673067e-10 ,1.1691977731059219042250488725954413609266959171312e-10 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

Verification of convexity for period-tupling bifurcation is skipped, as indicated by the flag in the config file.
Bound on Jacobi constant: [2.9940756819941148370203478568346157608182729552993 ,2.9940756819941148370203478568359159317502220759093 ]
dat/JupiterL1_07_PQ.dat at {9.8817483271490040629854411278790101774226774803133e-1 ,0 ,1.2905155266141899466594705780827733803044348148477e-1 ,0 ,1.4857887018896643133050011501406532414084522212085e-2 ,0 } completed.
Final result: false
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 12:09:18 2018
elapsed time: 1hours 33minutes 22seconds