Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/MoonL1_08_PD.dat at {-8.6033195753974808232941511780985641356268996658953e-1 ,0 ,1.1424338868796620859992161121759494887757428700904e-1 ,0 ,2.0120370209528317134493536805647033612776915772208 ,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]=[-5.0745361386068712972623382487143577432079243303252e-33 ,5.0745361301417983958645198426805449619507468483052e-33 ]
D0[i][3][0]=[8.4358694238392216286848363094065484435840801504565e-1 ,8.4358694238392216286848363094682667838752977425836e-1 ]
D0[i][3][2]=[-1.5863428085168146919927424559773199280737459978667e-30 ,1.5863428086161338492726054957469007567642666241196e-30 ]
dy0=[-1.0359034134602992600672260032602302525000566210282e-32 ,1.0754393980130852515592727258845606216774202664142e-32 ]
Ddy=[3.8136074350012249574008991606403006753832417639543 ,3.8136074350012488710555309927043466475734837020871 ]
dy=[-2.8200055101181116008004981417826637331148568760132e-33 ,2.7163346807875271531197102074449725734043535016148e-33 ]
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]=[-3.8949669749216033506972994718497529407512877461359e-31 ,3.8949669745297303364874565143271684022667581785582e-31 ]
D0[i][3][0]=[-1.7746784002458856225809501229871119635462152888184e-28 ,1.7746783987109109787769319024923089077417556042173e-28 ]
D0[i][3][2]=[-9.2591987054168654950733537449829094254947336505678e-29 ,9.2591987116792467187462130295306439045949380355326e-29 ]
dy0=[-3.8949669749216126104801477240261761006505477495922e-31 ,3.8984591418102751063352402397185332286775613104657e-31 ]
Ddy=[5.3927365835201048762831350374993742242464157727393 ,5.3927365835201325449153026670994140923400615506711 ]
dy=[-7.2290924680499761060956546717523427054620641147267e-32 ,7.2226167820330948838673619902207528964352128753711e-32 ]
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]=[3.8136074350012369142282150765924946264088007941113 ,3.8136074350012369142282150767521526965479246719301 ]
D0[i][5][0]=[7.9410700569574330240119247010117305237843627936059e-1 ,7.9410700569574330240119247010559250306320600523192e-1 ]
D0[i][3][0]=[8.4358694238392216286848363094065484435840801504565e-1 ,8.4358694238392216286848363094682667838752977425836e-1 ]
DBif[i][5][0]=[7.9410700569574330240119247010107647338438046088087e-1 ,7.9410700569574330240119247010568908205726182371164e-1 ]
DBif[i][3][0]=[8.4358694238392216286848363094021517935658427942162e-1 ,8.4358694238392216286848363094726634338935350988239e-1 ]
D[k][3][4]=[3.8136074350012353979960141992736834981173223544106 ,3.8136074350012384304604159540709638248394031116308 ]
_H(5,0,0)=[1.2446324454159258764732124457556412221957380982313e2 ,1.2446324454228027053658501172786107769639585802980e2 ]
_H(5,0,2)=[1.8428720345204535122707989910707016309204263058139e2 ,1.8428720345255406230062769846886215316179276142840e2 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[5.3927365835201187105992188518380373284344316449584 ,5.3927365835201187105992188527607509881520456784520 ]
D0[i][5][0]=[-1.3193904035809174256193721269225890617666431218648e-29 ,1.3193904043014781516035922311266648290360077009334e-29 ]
D0[i][3][0]=[-1.7746784002458856225809501229871119635462152888184e-28 ,1.7746783987109109787769319024923089077417556042173e-28 ]
DBif[i][5][0]=[-1.5181421834513456246122559443190827979063053020444e-29 ,1.5181421841719063505964760485231585651756698811130e-29 ]
DBif[i][3][0]=[-1.7841539455366513493957699929082364155719176374471e-28 ,1.7841539440016767055917517724134333597674579528460e-28 ]
D[k][3][4]=[5.3927365835201185995672641429784358069133762542907 ,5.3927365835201188216311735616203525096731010691197 ]
_H(5,0,0)=[-6.0879133753769787214190103842738499124324436611887e-9 ,6.0879133753769776798227737248303610586460347926004e-9 ]
_H(5,0,2)=[4.1797639838382694342718169301113294854426060003166 ,4.1797639958631710927395964162846410398701712419970 ]
g=[-1.8094594472574835760327745053546330532624314976454e-28 ,1.8094594487560990745152728920269469558680669028993e-28 ]
Dg=[4.1797639838382694342718162296823872231901210010020 ,4.1797639958631710927395971167135833021227091361094 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-4.3290947904060263548833021162732312873777694184939e-29 ,4.3290947868206193695196869617693834901759246302870e-29 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

T1={[-1.1505238315236051426193715036727163483537465254792e-16 ,1.1505238315236050557344330986863629793371294396051e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.2951373481206919012558576494854983216007009329514e-17 ,1.2951373481206918788087950726468817551365745117520e-17 ],[0 ,0 ]}
DH[2]=[4.4796418452349729915168309392392588535793524151702e-1 ,4.4796418452349729915168309437708059583821596042146e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[4.4796418452349724680928835215662327439598130235159e-1 ,4.4796418452349735149407783614438411398813100265052e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[5.3927365835201187105992188513573694721881580610492 ,5.3927365835201187105992188532414188440002245167216 ]
_H(5,0,0)=[-1.1132444123591854872779308427050717602035690089823e-15 ,1.1132444145690126149261688119137436700930273391099e-15 ]
_H(5,0,2)=[4.1797639898507192055695123937834465112937793665094 ,4.1797639898507213214419006502079374001182534931041 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.6634145307538578957684949073136259456891292712300e-16 ,2.6634145254668916148633325518124383696801101923817e-16 ],[0 ,0 ],[-6.7040451648948151160980853918268583795709133318602e-17 ,6.7040451782025673993200818751078815655911404852075e-17 ],[0 ,0 ]}
DH*T2=[-3.9025240932241621999942302360762232152843488004786e-16 ,3.9025240854775222935756345595171216811196769585886e-16 ]
Does bound on derivative Jacobi(bifCurve(x)) contain zero:
isSingular(DH*T2): true
############################

T3={[0 ,0 ],[0 ,0 ],[-8.0008197364479008273307427646395256205755801620726e-1 ,-8.0008197331812335609179783471895891802359364393714e-1 ],[0 ,0 ],[7.8668109782527862285156845822983843978241277477878e-1 ,7.8668109782527951454561439039469004080100480457718e-1 ],[0 ,0 ]}
DH*T3 + T2*(D2H*T2)=[-3.8638274067207594725284465235488431521577403054145e-1 ,-3.8638274052573315431792690116891002709035569172591e-1 ]
Is second derivative Jacobi(bifCurve(x)) nonzero:
!isSingular(DH*T3 + T2*(D2H*T2)): true
############################

Bound on Jacobi constant: [-9.8650909103850289518360023185927244657870672149283e-1 ,-9.8650909103850289518360023165164127756400068542616e-1 ]
dat/MoonL1_08_PD.dat at {-8.6033195753974808232941511780985641356268996658953e-1 ,0 ,1.1424338868796620859992161121759494887757428700904e-1 ,0 ,2.0120370209528317134493536805647033612776915772208 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 12:39:52 2018
elapsed time: 2hours 3minutes 56seconds