Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL1_02_PT.dat at {9.3392119695700850069177046152717659365745811303045e-1 ,0 ,6.1861407591651480539885875988247157312677280889248e-2 ,0 ,1.0321764135025265024988849727703698214569637558704e-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]=[-5.0587098465514677526178869138965169424542594257877e-34 ,5.0591182251252433906334429003156125257862967004654e-34 ]
D0[i][3][0]=[7.9707939891914438599682968640343083209058150040814e-1 ,7.9707939891914438599682968640460840460557695879877e-1 ]
D0[i][3][2]=[-8.9726161235702719182690009339165938697323301301673e-31 ,8.9725852460010297467945631507120748452853368091409e-31 ]
dy0=[-8.5669312918527742624225137282405198506352287481428e-33 ,1.7248698035629480609678164447832771993299778779722e-33 ]
Ddy=[1.7825193199624013843341162450519023082601134597777e1 ,1.7825193199624089963084945997651662727755833233875e1 ]
dy=[-9.6765840585634195396292860602340531280074134995332e-35 ,4.8060804704397123925085346426631115828931523196565e-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
############################

y0[i][3]=[-2.9753795737402325364153728967142219630351265040181e-32 ,2.9754096760648523446457399898468844819973330183501e-32 ]
D0[i][3][0]=[9.6234645352404231838241410994463109324420145728517e-2 ,9.6234645352404231838241411047921492902285887771484e-2 ]
D0[i][3][2]=[-5.1946565917794709667633114180370688272988440402733e-29 ,5.1946527130615593078407386807608212155796933102867e-29 ]
dy0=[-9.0330255832048661734598562129929260308966625892223e-32 ,2.9901266527130201557427700289417177085484938374962e-32 ]
Ddy=[1.7473180211624386344334417515783792370382432914473e2 ,1.7473180211624484109561240607923261263952644494278e2 ]
dy=[-1.7112664188765007738157272256096402364234260507653e-34 ,5.1696517026679913183256470624277296449284170870862e-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
############################

y0[i][3]=[-7.2324771931420823631327304736400463995182994667509e-31 ,7.2325314516144402395045879458167029894803910753787e-31 ]
D0[i][3][0]=[-1.1851450306091527970016330761093675165549355189443e-27 ,1.1851467107308715795870423048757321007824528594100e-27 ]
D0[i][3][2]=[-2.8733027491161600982084308662164752820693879586520e-27 ,2.8733018893367794692029547643054223431216845181225e-27 ]
dy0=[-1.7986716236008895287578508958737810532479821394369e-30 ,7.2325314516147283324621643399537213457386215306308e-31 ]
Ddy=[3.1138643588111450144888325303347966002614324500470e3 ,3.1138643588124251638127384115478149725895574866755e3 ]
dy=[-2.3226867384731125672014170221812418515593552814047e-34 ,5.7763326090658994240318268089967460834981710136421e-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]=[1.7825193199624051903213054224078654795620072139941e1 ,1.7825193199624051903213054224092031014736895691711e1 ]
D0[i][5][0]=[-1.2909819841946814279172608854822979459015463041267 ,-1.2909819841946814279172608854804101115140314576578 ]
D0[i][3][0]=[7.9707939891914438599682968640343083209058150040814e-1 ,7.9707939891914438599682968640460840460557695879877e-1 ]
DBif[i][5][0]=[-1.2909819841946814279172608854823571162594179005070 ,-1.2909819841946814279172608854803509411561598612775 ]
DBif[i][3][0]=[7.9707939891914438599682968640337971040991863423175e-1 ,7.9707939891914438599682968640465952628623982497517e-1 ]
D[k][3][4]=[1.7825193199624043436581318679060706246028703102628e1 ,1.7825193199624060369844789769109979564328264729024e1 ]
_H(5,0,0)=[8.1170299726941528552027010677834551109963240175711 ,8.1170299728280512848238675577878574079370040464545 ]
_H(5,0,2)=[-3.3644205919086639635893352468748772538189501585661e1 ,-3.3644205918816801013762322701952362410225126569380e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[1.7473180211624435226947829061752704858125385874111e2 ,1.7473180211624435226947829061954348776209691534641e2 ]
D0[i][5][0]=[1.1406504605318321136828313123351295610695875954986 ,1.1406504605318321136828313123657778659769794450158 ]
D0[i][3][0]=[9.6234645352404231838241410994463109324420145728517e-2 ,9.6234645352404231838241411047921492902285887771484e-2 ]
DBif[i][5][0]=[1.1406504605318321136828313123341806591053252874934 ,1.1406504605318321136828313123667267679412417530210 ]
DBif[i][3][0]=[9.6234645352404231838241410993729714550959119110981e-2 ,9.6234645352404231838241411048654887675746914389020e-2 ]
D[k][3][4]=[1.7473180211624421340658962212200725304955027795170e2 ,1.7473180211624449113236695911506328329380049613581e2 ]
_H(5,0,0)=[-6.5096096887667820064046755691464077141081766578022 ,-6.5096096800985782579197249258661102077443486025396 ]
_H(5,0,2)=[-4.0691193211900283392571357277788126460709423409547e1 ,-4.0691193181967228121406366414119706526238517523690e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[3.1138643588117850891507854699779254669925190052018e3 ,3.1138643588117850891507854719046861058584709315208e3 ]
D0[i][5][0]=[-2.5882916132583393544454854534129853407373647155268e-27 ,2.5882918380819760011282202693292371053075363625659e-27 ]
D0[i][3][0]=[-1.1851450306091527970016330761093675165549355189443e-27 ,1.1851467107308715795870423048757321007824528594100e-27 ]
DBif[i][5][0]=[-2.5981062685608178401142936109031678813039658303886e-27 ,2.5981064933844544867970284268194196458741374774278e-27 ]
DBif[i][3][0]=[-1.1910976748850470310143958243173907769914343792550e-27 ,1.1910993550067658135998050530837553612189517197208e-27 ]
D[k][3][4]=[3.1138643588117815307723385712691891295442465596257e3 ,3.1138643588117886475292323706134224433067433770969e3 ]
_H(5,0,0)=[-4.0166507486430645652536146557533458797591342773993e-7 ,4.0166507486294621311067739989688812401759621850453e-7 ]
_H(5,0,2)=[1.3419047517459451523129558252193625982880005212335e2 ,1.3419047830128758118564341982004780803673365572505e2 ]
g=[-2.7316769262085706319391559512005951355426279179763e-27 ,2.7316769616635897674358485119895552390395609183686e-27 ]
Dg=[1.3419047517459451523129549275939556631551611420392e2 ,1.3419047830128758118564350958258850154999847485754e2 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-2.0356712785385247104675620910771739955477840711558e-29 ,2.0356712521171120957746375083856728380447403926840e-29 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

D1={
{[-3.8821218444731440454931519741456952284946797160695e-2 ,-3.8821218444731435332004024140747005425078188453399e-2 ],[-3.8794048739944757820057714462310251901530903658023e2 ,-3.8794048739944757814180496893321577589226481746926e2 ],[7.9316093346552381165122206665548825686012703121047e-1 ,7.9316093346552382158533601483438861894533612757640e-1 ],[3.8625228398149006816623263973334749921908532308277e2 ,3.8625228398149006823050165117585603730756166400247e2 ],[8.6644986167472912867259561048341189499308049216415e2 ,8.6644986167472912881734431122836827203940828156032e2 ],[-3.2587416436218145354342133892306664217567634758245e1 ,-3.2587416436218145345303770656215384903375463650245e1 ]},
{[-1.4994363666255382776241922394919063894609554894059e-20 ,1.4994363666255382776241404913655955323418429390599e-20 ],[-2.3618175183374401290515359656971547427838494686694e-18 ,2.3618175183374401290513570475902348267356046050351e-18 ],[-2.3827042949314553266064357538517786556207911329762e-20 ,2.3827042949314553266064937820621908531597135832555e-20 ],[-2.3465068120595202801074650703835554523401047886467e-18 ,2.3465068120595202801076430220732851322226653570450e-18 ],[-5.2731070484552458859975116531633262341028607515744e-18 ,5.2731070484552458859979116959306985771634857920027e-18 ],[-2.0130291771801832141929026044397233027470060655057e-19 ,2.0130291771801832141927512261822728638814230459381e-19 ]},
{[3.4449468945830026578184578961555834291922034332581e-1 ,3.4449468945830026895478708107271597237293023050868e-1 ],[-2.3952260705298965589561579574819633398976609824645e2 ,-2.3952260705298965585872390518914690936001643302047e2 ],[-5.3381885202617644036984464304078128846254098827494e-2 ,-5.3381885202617637880370363502284808009039918933548e-2 ],[2.3848027479575197902159344357570043271313627383171e2 ,2.3848027479575197906189203769305941412276851825433e2 ],[5.3435590851245893537428154110001189433424475587197e2 ,5.3435590851245893546503538678838429445162305912806e2 ],[-2.0120155527586034042756118182913930248086859575331e1 ,-2.0120155527586034037128539902847901907211760587988e1 ]},
{[-8.4002837207700722273202709914015869118668058306190e-18 ,8.4003525312856396365265100414461424692518984412886e-18 ],[-1.3952374197751044402008049838602940827256056676877e3 ,-1.3952374197751044399998658096558402141373652374799e3 ],[-1.6300077706481275784086384079013334660457049496797e-17 ,1.6300038728411235806799646471311828470763788631998e-17 ],[1.3881103748936434725864316967208081929540540954882e3 ,1.3881103748936434728053885611119306230438294652107e3 ],[3.1138643588117850889042631299987032609225567038380e3 ,3.1138643588117850893973090236038720606043154182080e3 ],[-1.1781119079559748085270663193156891753027301818548e2 ,-1.1781119079559748082245680030612422968026661337399e2 ]},
{[-9.4138679216313433553262579840024418376261316308020e-1 ,-9.4138679216313431899454253367805978817730647205340e-1 ],[1.2347177429094550710439055906929685382515502967947e3 ,1.2347177429094550712397488601529350263893557004617e3 ],[-2.2815139296614181871522091690151058674279849011132 ,-2.2815139296614181550888089332888742738047029282292 ],[-1.2293446127993043348664941009691616410580085094152e3 ,-1.2293446127993043346530163611208894944867624933223e3 ],[-2.7562806582425740808055104465382394343694681526069e3 ,-2.7562806582425740803247716333219828831548767076157e3 ],[1.0371761282020558302441951580636112334048424272227e2 ,1.0371761282020558305406159718289307242273351174108e2 ]},
{[-1.6461285721585604783936589705878315187829680486510e-18 ,1.6461365469785462930865127354172129670355293197066e-18 ],[-1.5615645917368696895176182436328196030189855844095e2 ,-1.5615645917368696889790108365083636218619155981186e2 ],[-3.1687086401689271530029584158698204420113817411165e-18 ,3.1687042986601561229190354400332349441151569797576e-18 ],[1.5718624827195708298304680787051334020412925831874e2 ,1.5718624827195708304021477330035493472930317090452e2 ],[3.5096754131171907527382479039979083452620036128906e2 ,3.5096754131171907540253747603357407830586494490686e2 ],[-1.2129728914571332944345323564854188891004400606163e1 ,-1.2129728914571332937226271461194473215016836602127e1 ]}
}
D[2]={
{[-3.8821218444731440738509845005114536655118305858450e-2 ,-3.8821218444731435048425231377216039139023263969576e-2 ],[-3.8794048739944757845138688317432093360477408019895e2 ,-3.8794048739944757789099377314631553809139241309352e2 ],[7.9316093346552381075465636470888806688768252751691e-1 ,7.9316093346552382248189883712439370490068571950300e-1 ],[3.8625228398149006791411185806730643067256636532475e2 ,3.8625228398149006848262098208169651056784014724145e2 ],[8.6644986167472912810650586880878550235256974771413e2 ,8.6644986167472912938343079805170765139305967300841e2 ],[-3.2587416436218145377076074136081933817567517460904e1 ,-3.2587416436218145322569707952116071175317204436119e1 ]},
{[-9.7687633928043487474732451802009297578911217642122e-18 ,9.7687633928043487477314635061787818332020939740102e-18 ],[-6.2739267462131113112475824757902291664161527671637e-16 ,6.2739267462131113110817433826959955336452934379558e-16 ],[-1.9741199748020942942677794832448890054042534542159e-17 ,1.9741199748020942943199615184396732332973867368229e-17 ],[-6.3842514002675017141075850773719627698933564706346e-16 ,6.3842514002675017142763403888593038077656090175165e-16 ],[-1.4340887310098673613248503417893947856987945637354e-15 ,1.4340887310098673613627576977703819251617195951010e-15 ],[-6.2469952728772565015087718790908706002169602346984e-17 ,6.2469952728772565013436446672943275265252358059637e-17 ]},
{[3.4449468945830026559746181740134698326878673490169e-1 ,3.4449468945830026913917118251470279726794730344877e-1 ],[-2.3952260705298965610897234021744696972760037966396e2 ,-2.3952260705298965564536696274456250969108728849228e2 ],[-5.3381885202617644865771465290767118214694296212939e-2 ,-5.3381885202617637051583815492965124346947996164763e-2 ],[2.3848027479575197880736806373527388754952383166532e2 ,2.3848027479575197927611702061545818828952103438439e2 ],[5.3435590851245893489326241768026347670691647835907e2 ,5.3435590851245893594605362044101367177460777171139e2 ],[-2.0120155527586034062016991200472785599537808613847e1 ,-2.0120155527586034017867633865727903436391211568667e1 ]},
{[-1.2416354506257355491163360734156279045457844092879e-17 ,1.2416425683357170861242078815819451763918986809874e-17 ],[-1.3952374197751044421850800168610646186086391924752e3 ,-1.3952374197751044380155881206978614120385650822997e3 ],[-2.7063843844230113295062081177260480598320878009678e-17 ,2.7063795017481509610178915268378920442877455810985e-17 ],[1.3881103748936434705894706928847435073341767235430e3 ,1.3881103748936434748023469181282360895489074090593e3 ],[3.1138643588117850844204606362006859063259179554246e3 ,3.1138643588117850938811055785090121982665289806423e3 ],[-1.1781119079559748103480261931134093431706020612928e2 ,-1.1781119079559748064036059137211820373358012494742e2 ]},
{[-9.4138679216313433839264296714669266324987610592158e-1 ,-9.4138679216313431613452843582647227127638628498351e-1 ],[1.2347177429094550690692731244782949917049875039009e3 ,1.2347177429094550732143790462378106396932368546662e3 ],[-2.2815139296614181957242887868575649976893527722523 ,-2.2815139296614181465167249103698057260133571068072 ],[-1.2293446127993043368527946154776007254242631462508e3 ,-1.2293446127993043326667135760448521599841851934528e3 ],[-2.7562806582425740852655495363278649127909111441288e3 ,-2.7562806582425740758647274470306800654371465158917e3 ],[1.0371761282020558284340970072304247652816770949642e2 ,1.0371761282020558323507122103084103726682923377407e2 ]},
{[-3.0144284342807026931025229007544885926178778709672e-17 ,3.0144293871528616309303599698097203073620237349428e-17 ],[-1.5615645917368697146863313819699164566231905391421e2 ,-1.5615645917368696638103103106094400069427808717266e2 ],[-6.1593822713451685051070310726449108066000291607719e-17 ,6.1593819096839844284169165939763148801883734448590e-17 ],[1.5718624827195708043579971591813784837537741123787e2 ,1.5718624827195708558746312163886685209047931571722e2 ],[3.5096754131171906955337385971805877024835846403601e2 ,3.5096754131171908112299122185789773165428118735199e2 ],[-1.2129728914571333185485097577373705724088500095406e1 ,-1.2129728914571332696086602998330798590205192937410e1 ]}
}
Check intersection of two enclosures of hessian at bif point:intersection(H1,H[2],H[2]): true
############################

Check intersection of two enclosures of derivative at bif point:intersection(D1,D[2],D[2]): true
############################

T1={[-2.2347609068036977684806554695279297513910397663931e-16 ,2.2347609068036982444689386655034175624701449516220e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-6.9073265900812120677455892414182333530045050571308e-17 ,6.9073265900812134746893387902916774213504807148709e-17 ],[0 ,0 ]}
DH[2]=[-4.2666032927281347359649533599266603833740702338310e-1 ,-4.2666032927281347359649533541648057365235752570513e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-4.2666032927281348127242034331772607056798596177265e-1 ,-4.2666032927281346592057032809142210492839525522433e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[3.1138643588117850891507854627342367633804982558857e3 ,3.1138643588117850891507854791483749034878768022817e3 ]
_H(5,0,0)=[-2.6935270473401860639104649815940765678900059722155e-15 ,2.6935274383210413322907683704518654491458188879816e-15 ]
_H(5,0,2)=[1.3419047673794104018128271996154234876795655540311e2 ,1.3419047673794105624372720238407827269107314325611e2 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.0072418727457079573939598002288282328698557451130e-17 ,2.0072415813831129560198390790685940507894510687172e-17 ],[0 ,0 ],[-4.5795496281244839874047885319196329713378324686912e-17 ,4.5795502928723030652418655002634556514780652612527e-17 ],[0 ,0 ]}
DH*T2=[-3.9071574865194198732810847096638252717929176914922e-6 ,-3.9071574864921145630221739351551219191831529653398e-6 ]
Is Jacobi integral monotone along bifurcation curve:
!isSingular(DH*T2): true
############################

Bound on Jacobi constant: [3.0154129457133420189183052564322997736578975211393 ,3.0154129457133420189183052564992794868686989691713 ]
dat/JupiterL1_02_PT.dat at {9.3392119695700850069177046152717659365745811303045e-1 ,0 ,6.1861407591651480539885875988247157312677280889248e-2 ,0 ,1.0321764135025265024988849727703698214569637558704e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 10:50:07 2018
elapsed time: 0hours 14minutes 11seconds