Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL2_05_PQ.dat at {9.9904573480783192068800697065051789266708597726768e-1 ,0 ,4.4682462050745463614132211719985627749543152192802e-5 ,0 ,6.5319411473527641718660751672455819262075862729277 ,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]=[-3.4371908749262414508054664012872644818139362965307e-51 ,-3.4055551864169409976708665376481648981312075164696e-51 ]
D0[i][3][0]=[-8.4404763257189973067022157264342178017143963066954e-4 ,-8.4404763257189973067022157264342178017143963066767e-4 ]
D0[i][3][2]=[3.9233283539765907810666159812448535625694090559793e-50 ,4.1094209668044368585402281621951513879667644689334e-50 ]
dy0=[-3.8868329154822082906166718772234105751116386556346e-51 ,-2.9559131474291894269123465261656432424954127169673e-51 ]
Ddy=[1.7291350926003106190140942215969975376167744993341e5 ,1.7291350926003106190140942215995569858408760147577e5 ]
dy=[1.7094749624125802277323483047612216354210580342695e-56 ,2.2478480322998390960289075016946610324024271014182e-56 ]
r[4]=[-9.9999999999999999998178723819146466463082237946491e-46 ,9.9999999999999999998178723819146466463082237946491e-46 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-1.2202149183470920316209412372967195296930022860651e-47 ,3.2073932754081797990103394250953370408846015415309e-47 ]
D0[i][3][0]=[1.9994674333360490132307019625051699122106720460818 ,1.9994674333360490132307019625051699122106720598103 ]
D0[i][3][2]=[-6.1671612956068707226472989352951094598211245479988e-43 ,6.1648442061892693076474722991768038413039917448406e-43 ]
dy0=[-1.3267307805947410346596420939174540116902081135751e-47 ,3.3139091381017674984879495959662185130714376613178e-47 ]
Ddy=[-4.9170990963689526434725538895736328139218671855447e8 ,-4.9170990963689526434725538895618112939237081152006e8 ]
dy=[-2.6981981745587953872467844971732277360448786907102e-56 ,6.7395614226057273632305634008454356037880908462877e-56 ]
r[4]=[-9.9999999999999999998178723819146466463082237946491e-46 ,9.9999999999999999998178723819146466463082237946491e-46 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-9.1693345371181712021097880535392077399579372369146e-44 ,9.1693335385908735979137174246103596514744858918106e-44 ]
D0[i][3][0]=[-8.4404763257189973067022157264342178025344018180893e-4 ,-8.4404763257189973067022157264342178008943841562491e-4 ]
D0[i][3][2]=[-8.8517827170444735664122860807331718895755646236071e-39 ,8.8517827171570038586479368538109079480162184278439e-39 ]
dy0=[-9.1693345820823753215902777002360589002736918056655e-44 ,9.1693335835550774966888760052654227494567240438800e-44 ]
Ddy=[2.4336289880304284157609822918484479429306357041533e5 ,2.4336289880304284157609822918531500968849981265391e5 ]
dy=[-3.7677614906189761754942176983358725832865003052992e-49 ,3.7677619009228075056034833621841039555479879083478e-49 ]
r[4]=[-9.9999999999999999998178723819146466463082237946491e-46 ,9.9999999999999999998178723819146466463082237946491e-46 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-1.2810478441818152873239918778954252163212117832204e-37 ,1.2810478443198873273885920895866944475899320702010e-37 ]
D0[i][3][0]=[-1.1487195367214403491143477673993505369545586923782e-34 ,1.1487195362632861492280796014390238099935786898071e-34 ]
D0[i][3][2]=[-1.9478899753135055838659814469319836721313065794698e-32 ,1.9478899753134913542289127617798542902926253423948e-32 ]
dy0=[-1.2810478441818152873239922090367210196347500864849e-37 ,1.2810478443198873274166608603929236221544598783766e-37 ]
Ddy=[-3.0953087137997595083442980489353603356879636919839e8 ,-3.0953087137997595083442980489252165703199130045194e8 ]
dy=[-4.1386755333015494805445273047693610788726195002172e-46 ,4.1386755337476182021460416969417935777968026534529e-46 ]
r[4]=[-9.9999999999999999998178723819146466463082237946491e-46 ,9.9999999999999999998178723819146466463082237946491e-46 ]
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]=[1.7291350926003106190140942215982772616574212881340e5 ,1.7291350926003106190140942215982772618002292259577e5 ]
D0[i][5][0]=[1.7393660333082281429566103532276863850397058875637e-2 ,1.7393660333082281429566103532276863850397058875669e-2 ]
D0[i][3][0]=[-8.4404763257189973067022157264342178017143963066954e-4 ,-8.4404763257189973067022157264342178017143963066767e-4 ]
DBif[i][5][0]=[1.7393660333082281429566103532276863850134084038803e-2 ,1.7393660333082281429566103532276863850660033712503e-2 ]
DBif[i][3][0]=[-8.4404763257189973067022157264342178021508213642339e-4 ,-8.4404763257189973067022157264342178012779712491382e-4 ]
D[k][3][4]=[1.7291350926003106190140942215969975377178990805084e5 ,1.7291350926003106190140942215995569857397514335833e5 ]
_H(5,0,0)=[-1.6465872961755347444189596645206502342207147423990e-3 ,-1.6465872961755347444184665702841240823057412198591e-3 ]
_H(5,0,2)=[-3.7680723341869398091783548064099542392878569354739e-3 ,-3.7680723341869398091773874066808725052614279631559e-3 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-4.9170990963689526434725538895677220539441565567125e8 ,-4.9170990963689526434725538895677220539014187440328e8 ]
D0[i][5][0]=[4.2749214879372061005476177115329755512507434799871e-2 ,4.2749214879372061005476177115329755512508141136526e-2 ]
D0[i][3][0]=[1.9994674333360490132307019625051699122106720460818 ,1.9994674333360490132307019625051699122106720598103 ]
DBif[i][5][0]=[4.2749214879372061005476177115329755512188331435912e-2 ,4.2749214879372061005476177115329755512827244500485e-2 ]
DBif[i][3][0]=[1.9994674333360490132307019625051699121046272114023 ,1.9994674333360490132307019625051699123167168944898 ]
D[k][3][4]=[-4.9170990963689526434725538895736328138916106376880e8 ,-4.9170990963689526434725538895618112939539646630573e8 ]
_H(5,0,0)=[-7.4389266608949258574814037521176323594467138969228e-3 ,-7.4389266336228940876532747251872718451858544117429e-3 ]
_H(5,0,2)=[-6.7998694648682221860842747700688359183078702808948e-3 ,-6.7998694472986436454590383694429946997948049405595e-3 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[2.4336289880304284157609822918507989510511228182967e5 ,2.4336289880304284157609822918507990887645110123957e5 ]
D0[i][5][0]=[1.7393660333082281429566103532276863849004976738090e-2 ,1.7393660333082281429566103532276863851789064115844e-2 ]
D0[i][3][0]=[-8.4404763257189973067022157264342178025344018180893e-4 ,-8.4404763257189973067022157264342178008943841562491e-4 ]
DBif[i][5][0]=[1.7393660333082281429566103532276863846775931392297e-2 ,1.7393660333082281429566103532276863854018109461636e-2 ]
DBif[i][3][0]=[-8.4404763257189973067022157264342178026098951683088e-4 ,-8.4404763257189973067022157264342178008188908060296e-4 ]
D[k][3][4]=[2.4336289880304284157609822918484479429890137009272e5 ,2.4336289880304284157609822918531500968266201297652e5 ]
_H(5,0,0)=[-1.6236884013020187799583107409704232895760483632434e-2 ,-1.6236702897507061452654396673230857260073777305651e-2 ]
_H(5,0,2)=[-9.7236485270682694650507312874661774014239214369138e-3 ,-9.7235118337479205711368758965661713429911772322698e-3 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-3.0953087137997595083442980489304398544230007223673e8 ,-3.0953087137997595083442980489301370515848759741360e8 ]
D0[i][5][0]=[-3.2083051079321016441274744645949752467413044263939e-33 ,3.2083051078008656489015634268690043286041080813569e-33 ]
D0[i][3][0]=[-1.1487195367214403491143477673993505369545586923782e-34 ,1.1487195362632861492280796014390238099935786898071e-34 ]
DBif[i][5][0]=[-3.2083103684302891689146929877018630305743834482062e-33 ,3.2083103682990531736887819499758921124371871031692e-33 ]
DBif[i][3][0]=[-1.1496790112600788558182730733290285686427211445263e-34 ,1.1496790108019246559320049073687018416817411419552e-34 ]
D[k][3][4]=[-3.0953087137997595083442980489353603346434013176403e8 ,-3.0953087137997595083442980489252165713644753788630e8 ]
_H(5,0,0)=[-2.8326481013757593164819736019385572285137438659433e-3 ,2.8326481013804760678864232078168299126531019718040e-3 ]
_H(5,0,2)=[-2.2423448597966371787077182041501802759887046019854e-2 ,-1.0193013625117382756116160102355155508079922627431e-2 ]
g=[-3.2103720373111934554755769943035934423539233425897e-33 ,3.2103720371791358724435679308851036735689294212705e-33 ]
Dg=[-2.2423448597966371787077182042101939705213533846561e-2 ,-1.0193013625117382756116160101755018562753434800709e-2 ]
r[2]=[-1.7000000000000000000367675156905434163039627783854e-30 ,1.7000000000000000000367675156905434163039627783854e-30 ]
Dg!=0.: true
############################

-g/Dg=[-3.1495808358386480696609870597448920805656342978733e-31 ,3.1495808357090911124264790089945245566319809509012e-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={[-2.1186427817631645139541556039480854398307149873355e-28 ,2.1186427817631645140069085958250656729533687679711e-28 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.1704017176817857456852277477611531731664710039093e-35 ,1.1704017176817857462904350466489533284661576378285e-35 ],[0 ,0 ]}
DH[2]=[-1.2255985790350515049188861506717008152895100793576e-3 ,-1.2255985790350515049188861343009589974242134749023e-3 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-1.2255985790350515049188861618545121365866135846822e-3 ,-1.2255985790350515049188861231181476761271099753603e-3 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[-3.0953087137997595083442980489313433124898170171999e8 ,-3.0953087137997595083442980489292335935180968427500e8 ]
_H(5,0,0)=[-1.8758191094756155633233176340878204780295867200545e-10 ,1.8758191094756155351665185086739727669019184179144e-10 ]
_H(5,0,2)=[-1.6308231487994279098478919096749742636351843890890e-2 ,-1.6308230735099930051003010545117501146120142820770e-2 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.1502284582216032305075169361149533664640155199812e-8 ,1.1502284582216032132421252558191603452305708185944e-8 ],[0 ,0 ],[-1.1502284581142924640893573619239330092215901018655e-8 ,1.1502284581142924813547490406089485345630798766457e-8 ],[0 ,0 ]}
DH*T2=[-1.0990062339839442726459038304946743777706713503328e-2 ,1.0990062339839442561493783754748157799262718804805e-2 ]
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: [3.0243505410793426055378539845549146313947200865183 ,3.0243505410793426055378539845713737052083998667854 ]
dat/JupiterL2_05_PQ.dat at {9.9904573480783192068800697065051789266708597726768e-1 ,0 ,4.4682462050745463614132211719985627749543152192802e-5 ,0 ,6.5319411473527641718660751672455819262075862729277 ,0 } completed.
Final result: false
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 13:42:32 2018
elapsed time: 3hours 6minutes 36seconds