Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL2_03_PD.dat at {1.0081664029013508603758177260758981360962726311010 ,0 ,2.9189907458117540288400949254900560838772260773855e-2 ,0 ,2.2098073277808221686481479735058604290699683364288e-1 ,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]=[-8.7042475330979640190865042429167358179578046513092e-34 ,8.7042472502767335678236989438894536757137159557545e-34 ]
D0[i][3][0]=[8.6018337403314842738225993892200518162571425933568e-2 ,8.6018337403314842738225993893085423611999686493188e-2 ]
D0[i][3][2]=[-3.8425476230137181416243702542418156327672159181938e-31 ,3.8425479286501339081396873547677869500529928978480e-31 ]
dy0=[-1.3548775865147257491282390806234443906014985651517e-33 ,9.9842322242700312901780335495652806766426291009351e-34 ]
Ddy=[3.5662247538307451205559836558708224073049459993579e1 ,3.5662247538307501446821435026570724253738941307170e1 ]
dy=[-2.7996643266931594346384253264958095022193082329184e-35 ,3.7991929282060862034862291150740429368697188708735e-35 ]
r[4]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
subset(dy,r[4])=true
Validate the existence of Lyapunov-Schmidt reduction in the considered domain:
computeLyapunovSchmidtReduction(i): true
############################

y0[i][3]=[-3.1824387602321993505773771993500399318982400415687e-32 ,3.1824388731490150613852843518068508836483083339903e-32 ]
D0[i][3][0]=[-4.0919890307727464230340929587673027763416267860999e-29 ,4.0919889844714809184563898740339689514143805819428e-29 ]
D0[i][3][2]=[-6.6819375634852994550138062689925551484169922322819e-29 ,6.6819375834746644154558522256059925617599396554058e-29 ]
dy0=[-3.4442248294199220235436483235766469064576040612090e-32 ,3.1824388731490827604491532281435342692155827091043e-32 ]
Ddy=[2.9921007328596516737553924159498905615887032298829e2 ,2.9921007328598994212554828542848994028925082499991e2 ]
dy=[-1.0636135468967044103615732535980662022005443945622e-34 ,1.1511059074966904902633466650214550545503730113982e-34 ]
r[4]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
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]=[3.5662247538307476326190635792635193798560918020305e1 ,3.5662247538307476326190635792643754528227483280445e1 ]
D0[i][5][0]=[1.1156032407522089571250064207816859744868172704638 ,1.1156032407522089571250064207822638877308434175740 ]
D0[i][3][0]=[8.6018337403314842738225993892200518162571425933568e-2 ,8.6018337403314842738225993893085423611999686493188e-2 ]
DBif[i][5][0]=[1.1156032407522089571250064207815666973682997562583 ,1.1156032407522089571250064207823831648493609317796 ]
DBif[i][3][0]=[8.6018337403314842738225993892068376843634792451959e-2 ,8.6018337403314842738225993893217564930936319974796e-2 ]
D[k][3][4]=[3.5662247538307476114872284952168747867690173798398e1 ,3.5662247538307476537508986633110200459098227502351e1 ]
_H(5,0,0)=[3.1922581031365413701796049094761079723879937582328 ,3.1922581032463100898636590801067235669758320289462 ]
_H(5,0,2)=[1.2095823658254116394622671837354406302149975876208 ,1.2095823660099776948988036221136005183597171638752 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[2.9921007328597755475054376350073128687461341169874e2 ,2.9921007328597755475054376352274770957350773628946e2 ]
D0[i][5][0]=[-9.7493023515892148758135697079670142191880823453944e-29 ,9.7493023392009863744011462389254386708003009336851e-29 ]
D0[i][3][0]=[-4.0919890307727464230340929587673027763416267860999e-29 ,4.0919889844714809184563898740339689514143805819428e-29 ]
DBif[i][5][0]=[-9.7868679188131336685449673010199985726345090907849e-29 ,9.7868679064249051671325438319784230242467276790756e-29 ]
DBif[i][3][0]=[-4.1969812330798547703952124544603782636068853324004e-29 ,4.1969811867785892658175093697270444386796391282433e-29 ]
D[k][3][4]=[2.9921007328597750515235446529473653131773069434761e2 ,2.9921007328597760434873306172874246513039045364059e2 ]
_H(5,0,0)=[-1.6795008553922730459615760976794335015122697867171e-8 ,1.6795008553919195244991378559779762210168443949429e-8 ]
_H(5,0,2)=[-2.8818097512416559247502334812104745321825490322983e1 ,-2.8818097424696435008353566145945369070430250806498e1 ]
g=[-1.1029897416217819992775567673864162438935235802744e-28 ,1.1029897417945027409796839161058160756602109219653e-28 ]
Dg=[-2.8818097512416559247502336547353552263831769097749e1 ,-2.8818097424696435008353564410696562128423972938522e1 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-3.8274204065829328693619482363147202237624932407318e-30 ,3.8274204071822810468516582807810909387689603890170e-30 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

T1={[-1.0331931665117922475685249582678507733928300591493e-16 ,1.0331931665117922481084411427543590057473002230925e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.0508286995072215280163097341422639694471413682831e-18 ,2.0508286995072205264321681509027849581066631191614e-18 ],[0 ,0 ]}
DH[2]=[7.0048338619796225758014878854935935244839165879655e-2 ,7.0048338619796225758014878980998269632354843816299e-2 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[7.0048338619796221431595089804231547456234378839014e-2 ,7.0048338619796230084434668031704770358745017955410e-2 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[2.9921007328597755475054376348174797469952809377419e2 ,2.9921007328597755475054376354173102175156571264874e2 ]
_H(5,0,0)=[-1.1228674452356479945921623325489725337695337788495e-15 ,1.1228674515514649486290760759980848066591861741180e-15 ]
_H(5,0,2)=[-2.8818097468556499098576403384569007086720559573572e1 ,-2.8818097468556495157288523643676468983663473003557e1 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-3.8963968612459990821715625672345835860198364668533e-17 ,3.8963968831621472974662011840312224470590624364626e-17 ],[0 ,0 ],[-3.7947404374130430332496224752591692304397395503055e-17 ,3.7947404160686840373032880792675242531501897469676e-17 ],[0 ,0 ]}
DH*T2=[-8.2783049000253128686568302553756167647591604027735e-17 ,8.2783049465884745847187907854881763871197466344834e-17 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[9.0331258140065786871810418194618434725467024879169 ,9.0331280536480986818213645012743518709450204560803 ],[0 ,0 ],[1.3432471355054431112973844200589279728433992280043 ,1.3432471355054439350330973244408989752129171481516 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-1.6060937280177566753799660748671549403890107224101e-3 ,-1.6059368448424932209579494918494945130064058508781e-3 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [3.0091557491590008844773187520395790972511841556764 ,3.0091557491590008844773187520514149778191787644487 ]
dat/JupiterL2_03_PD.dat at {1.0081664029013508603758177260758981360962726311010 ,0 ,2.9189907458117540288400949254900560838772260773855e-2 ,0 ,2.2098073277808221686481479735058604290699683364288e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 11:38:45 2018
elapsed time: 1hours 2minutes 49seconds