Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL1_04_PT.dat at {9.5024214388859370577645905233401410860214480973371e-1 ,0 ,8.1676422659915674194420062246092845856184813324511e-2 ,0 ,1.0010076870391574821367119426714994541793583524600e-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]=[-1.6005143211669583390195528760460841413197788666121e-33 ,1.6005124243189406816489707369208236964841198758666e-33 ]
D0[i][3][0]=[2.3325711823944288085726547967834830226253707518372 ,2.3325711823944288085726547967869043216953580951728 ]
D0[i][3][2]=[-3.3417967036470695067760256433719955824242184097043e-30 ,3.3417976092671087874813035941542291234314743278323e-30 ]
dy0=[-1.7932803526821687177004704046251123096232412088007e-32 ,9.9200889900063733771307355360549866558687640539332e-33 ]
Ddy=[4.9645599582570133861291237286006768206789435700862 ,4.9645599582570167886977002561819530844005538610205 ]
dy=[-1.9981809210516969916133355801943363127303755332756e-33 ,3.6121637521964061935093713901775173480868011978328e-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]=[-2.0351254974656398834706168099367071307082934014956e-31 ,2.0351254884876168840796626198951207555194813796671e-31 ]
D0[i][3][0]=[3.0922785914182004162160218746069544781844195781119e-1 ,3.0922785914182004162160218777013095239153499648262e-1 ]
D0[i][3][2]=[-6.7562918582309349509972101889131582988753585474603e-28 ,6.7562918694105973092562973950308371276509385385750e-28 ]
dy0=[-2.1778112875358091963947078128854941308983055750278e-31 ,2.0461547118176799114246333953550016264440391540603e-31 ]
Ddy=[9.9868674313865283183311415254276393302005101732932 ,9.9868674313865394193532536770540949012211754233665 ]
dy=[-2.0488453720603775938981215285810732011434858504347e-32 ,2.1806750740391598670408028297812696195867144632912e-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
############################

y0[i][3]=[-1.1738290577605882012237629682220460990869230905307e-29 ,1.1738290576299955968716990206188833463264760300039e-29 ]
D0[i][3][0]=[-1.0793097746883077084273577750276212654863497275236e-26 ,1.0793097746637670286501081341088952938345862448983e-26 ]
D0[i][3][2]=[-8.4241764637434331222793402146896293049797343980465e-26 ,8.4241764644039355441982310892136728218124797205149e-26 ]
dy0=[-1.1751574094973824496881690842570146317572260062569e-29 ,1.1738290576300798391403574814793879015748168626038e-29 ]
Ddy=[1.0238282113100529270504725870785566321395003770074e1 ,1.0238282113102340110956744215869371205364930194233e1 ]
dy=[-1.1465097803156755619634786316577105096060059389919e-30 ,1.1478072165971029904474682644383893253688542115395e-30 ]
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]=[4.9645599582570150874134119923506116326369928901374 ,4.9645599582570150874134119924320182724425045409693 ]
D0[i][5][0]=[-1.0937399574679173560347047718443501080689690408000 ,-1.0937399574679173560347047718354722600348620871597 ]
D0[i][3][0]=[2.3325711823944288085726547967834830226253707518372 ,2.3325711823944288085726547967869043216953580951728 ]
DBif[i][5][0]=[-1.0937399574679173560347047719054821836333189663417 ,-1.0937399574679173560347047717743401844705121616180 ]
DBif[i][3][0]=[2.3325711823944288085726547967557633704098631941196 ,2.3325711823944288085726547968146239739108656528904 ]
D[k][3][4]=[4.9645599582570137109163003255103094506840544248099 ,4.9645599582570164639105236592723204543954430062968 ]
_H(5,0,0)=[1.4191812298819842843130685846982915664742777653939e1 ,1.4191812299432129193805032444359363766125061993137e1 ]
_H(5,0,2)=[1.0843704075223274317275533309855807620316611132266e1 ,1.0843704077095979161984660862262641301685650463392e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[9.9868674313865338688421976002769992435535359950533 ,9.9868674313865338688421976022047349878681496016065 ]
D0[i][5][0]=[-1.7718080986518771322239719717118239283347044682827 ,-1.7718080986518771322239719715038583979408203541034 ]
D0[i][3][0]=[3.0922785914182004162160218746069544781844195781119e-1 ,3.0922785914182004162160218777013095239153499648262e-1 ]
DBif[i][5][0]=[-1.7718080986518771322239719718257579795356573425493 ,-1.7718080986518771322239719713899243467398674798368 ]
DBif[i][3][0]=[3.0922785914182004162160218736961396812148648801410e-1 ,3.0922785914182004162160218786121243208849046627972e-1 ]
D[k][3][4]=[9.9868674313865315676730864997863299655902630434737 ,9.9868674313865361700113087026954042658314225531861 ]
_H(5,0,0)=[1.3613939898335635637964983123347433105284261270119e1 ,1.3613939914663332157782295407945853602102102942189e1 ]
_H(5,0,2)=[-4.7253882598149736986515451034436643218064222690779e1 ,-4.7253882482671304145988189727694812742723451139789e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[1.0238282113101434690730734517141878107091007210520e1 ,1.0238282113101434690730735569513059419668926753786e1 ]
D0[i][5][0]=[-3.0497964225482344299178300528007196474788164440359e-26 ,3.0497964225428629834672752021677766374929040542333e-26 ]
D0[i][3][0]=[-1.0793097746883077084273577750276212654863497275236e-26 ,1.0793097746637670286501081341088952938345862448983e-26 ]
DBif[i][5][0]=[-3.1884008513795140133550616435488100197494597775322e-26 ,3.1884008513741425669045067929158670097635473877296e-26 ]
DBif[i][3][0]=[-1.0880346820578157253596854572311491984192481810600e-26 ,1.0880346820332750455824358163124232267674846984347e-26 ]
D[k][3][4]=[1.0238282113101395338268433218503624608404206125957e1 ,1.0238282113101474043193036868151312918355727838349e1 ]
_H(5,0,0)=[-1.5588045720765958092256401909901256879038832078042e-6 ,1.5588045720806000690259780168741966648434749787529e-6 ]
_H(5,0,2)=[-2.8289585819241865915468864342378711205289873717552e2 ,-2.8289582547873481383767223273316096527695940440801e2 ]
g=[-4.9404180435166913512947033666377277275690119849056e-26 ,4.9404180435514808431066503645531717176398970801239e-26 ]
Dg=[-2.8289585819241865915468935648244974996817802927892e2 ,-2.8289582547873481383767151967449832736165963035422e2 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-1.7463736112599727813300360157137883039175878467065e-28 ,1.7463736112722704148327835182828441075294935205161e-28 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

D1={
{[2.1070151558545282932802756166415337442521205475482e-1 ,2.1070151558545283088013980107086165784576578645231e-1 ],[-1.7822103616767821015653497532164118856096325861814 ,-1.7822103616767820949795105160965977459822608794563 ],[2.8829012975814847611237263304087459910129225726982e-1 ,2.8829012975814848211117817073149833532124843422978e-1 ],[2.2232136370037362691320541839740918560704513478552 ,2.2232136370037362761639385974426488997263544578283 ],[7.6162452012162452671128442787383490786262474193249 ,7.6162452012162452722190211867191422827955223501484 ],[3.8801018795920968983714465786614494645693542609170e-1 ,3.8801018795920969253620492051076922157767691568555e-1 ]},
{[-1.4817397002612548741878287875594156848068468178468e-20 ,1.4817397002612548741878712854725804645658932093783e-20 ],[-6.2250813828953059232292585474027334797937934039652e-20 ,6.2250813828953059232290618070059520305608445468115e-20 ],[-1.8829229218260574326864426762896097561051555184402e-20 ,1.8829229218260574326864793215571101013630881873003e-20 ],[-9.6512692945476668996109657976858091936564675586571e-20 ,9.6512692945476668996112625060334669543133711299843e-20 ],[-2.5741871785183979507689655632274678195885709194848e-19 ,2.5741871785183979507690655984218160386886774343337e-19 ],[-2.5058195133397879870910549195825170019908636641637e-20 ,2.5058195133397879870911290417247105529931346093159e-20 ]},
{[-1.2161506346494670973965245805924934724712041821244e-1 ,-1.2161506346494670688173401175403203045011042616059e-1 ],[-3.8008417834857745800034562222455395845657958273774 ,-3.8008417834857745676169785411135756833847947058729 ],[5.8948726620619431314347261726678628617796215441657e-1 ,5.8948726620619432443571256665550472400737359233624e-1 ],[4.7413501048153291062842547413923121101089523282601 ,4.7413501048153291194947537274274098567631315189383 ],[1.5789056329213983474279157633503051567952754305430e1 ,1.5789056329213983483861305469125500941113617400692e1 ],[8.2749229076752135673739719193697517919864623181296e-1 ,8.2749229076752136178133426894710349076237217427200e-1 ]},
{[-4.8240806658846017408822218961644022794649147778128e-18 ,4.8240809129616369177667358764004115480443800823003e-18 ],[-1.3133394818045465850398864821453152770643404485059e-2 ,-1.3133394818045425565809104881367402879907954624721e-2 ],[-1.8271518318298664478991121560813343611110524321782e-17 ,1.8271518560443783650128005374827483117786747822258e-17 ],[3.0387903997320992309711376245432936349465331424858 ,3.0387903997320992740652246944026545912147374069173 ],[1.0238282113101434674708558562759041159336537977946e1 ,1.0238282113101434706752915993013335432937909194181e1 ],[1.8468421239151528322071355986767034115964519226604 ,1.8468421239151528486346554602129860615820361966019 ]},
{[7.2114390865170352293692192868544849221980956470233e-1 ,7.2114390865170354239124107061427851713609691737753e-1 ],[2.6303244273512462993970932516241565544463645114015e1 ,2.6303244273512463077977365791402105605509217303974e1 ],[-4.1584229753340746058662180712748056336061818922324 ,-4.1584229753340745295231716667211012501879708847893 ],[-3.2811913017549125640407901988433991474356763624610e1 ,-3.2811913017549125550624737919691528000815277858510e1 ],[-1.0853157243472625090168539150624868313060325557482e2 ,-1.0853157243472625083524201641922931875002587506525e2 ],[-5.7265556154102879505742077590004876321523977871699 ,-5.7265556154102879162847968270745241401265438338344 ]},
{[-2.5649654905030902273200924299187178459399337841791e-18 ,2.5649654907146489374721686159379794539705038033282e-18 ],[-3.8498170991286733483642593418451169541299557946819 ,-3.8498170991286733259883498958518108422651517587875 ],[-9.8663994869257327255762515482302873353310403745570e-18 ,9.8663995611709198208296080171948280641671456525300e-18 ],[3.3852409662173703131013064091238474371828433353742 ,3.3852409662173703374447163253175446044788053655263 ],[1.6754996992362285118823438089718750187941701202336e1 ,1.6754996992362285139935812060503495311134500563225e1 ],[-2.6486582176162735751005404414252773946562919716877e-2 ,-2.6486582176162726733573611868864039542529411681861e-2 ]}
}
D[2]={
{[2.1070151558545282947407990711925169301864472467444e-1 ,2.1070151558545283073408745677219613312566996771296e-1 ],[-1.7822103616767821069601122212874394656787695084766 ,-1.7822103616767820895847480106836434925221567949281 ],[2.8829012975814847387799147378448268996595225482723e-1 ,2.8829012975814848434555931836913040720569366105314e-1 ],[2.2232136370037362625266107738205069557054043029870 ,2.2232136370037362827693819626749003093726563405859 ],[7.6162452012162452583006084045180766530961861968108 ,7.6162452012162452810312569421824640562427482307702 ],[3.8801018795920968908560807317840539624519622533044e-1 ,3.8801018795920969328774149981199761733801549368869e-1 ]},
{[-1.0933665707298935172166804656534578241310214520016e-17 ,1.0933665707298935172192999608996790945318463882817e-17 ],[-6.2575392637548421231614298080062745940648793121742e-17 ,6.2575392637548421231464379518500119248553841400473e-17 ],[-5.2454476349264342490478558610203586983726881395047e-17 ,5.2454476349264342490604229410023447674790480268601e-17 ],[-6.9244684504819555935975148196220176707728180122848e-17 ,6.9244684504819555936141045093694716669165329834852e-17 ],[-6.1009068886439298925668433007576193404886943259444e-17 ,6.1009068886439298925814598959785367110988585746671e-17 ],[-2.1754827791926948759115747000105490199442104218124e-17 ,2.1754827791926948759167867368067053813216296331378e-17 ]},
{[-1.2161506346494670957879572584516851052245377623658e-1 ,-1.2161506346494670704259077784433978986389469739661e-1 ],[-3.8008417834857745870737670546917764146099633731185 ,-3.8008417834857745605466677547179862608004814171110 ],[5.8948726620619431052922827252956519520181559428536e-1 ,5.8948726620619432704995696733658456009615265407276e-1 ],[4.7413501048153290973535079418930175439869441767127 ,4.7413501048153291284255005627023522591697482488370 ],[1.5789056329213983457064533976435748179959813434751e1 ,1.5789056329213983501075928959914914353999850195657e1 ],[8.2749229076752135594331543840156951044597134318112e-1 ,8.2749229076752136257541600345379572287115374264056e-1 ]},
{[-1.6915053618091409086422544799531060298095466425445e-17 ,1.6915053635929860153419468712484834513860346119615e-17 ],[-1.3133394818045567452178703119849564320415861120598e-2 ,-1.3133394818045323964029501876526748046034070222205e-2 ],[-9.0111341386486032375587572911652570760905750066758e-17 ,9.0111341988783901370206507820716224905899206861998e-17 ],[3.0387903997320991135145655314174348121394044852238 ,3.0387903997320993915217969308462640575847240920137 ],[1.0238282113101434530833530870445113140762170228351e1 ,1.0238282113101434850627942276223352377533574396560e1 ],[1.8468421239151528035925132127579739641045562981329 ,1.8468421239151528772492776995910979913234220985367 ]},
{[7.2114390865170352393338410780504566595699925837549e-1 ,7.2114390865170354139477912939452755468894111324116e-1 ],[2.6303244273512462930127816108299558553044559731646e1 ,2.6303244273512463141820482704600913559545468063254e1 ],[-4.1584229753340746293112901251070743732247139225387 ,-4.1584229753340745060781000260128446788356087626380 ],[-3.2811913017549125721810518861026502160485615932300e1 ,-3.2811913017549125469222121531039398763622452504382e1 ],[-1.0853157243472625109544233231314845532823608037908e2 ,-1.0853157243472625064148507526928459199758883122892e2 ],[-5.7265556154102879582643977235230672132086989088550 ,-5.7265556154102879085946067744686938067536906598594 ]},
{[-7.5351068410832065606603266318071285384930857505982e-17 ,7.5351068399100958092782038646730439101244428603332e-17 ],[-3.8498170991286738219951933523696438374615191763275 ,-3.8498170991286728523574158518090724198644956767806 ],[-3.8404710520810499727645087965695745824069733031518e-16 ,3.8404710527496597239285977132419216607358470097665e-16 ],[3.3852409662173697842097033322634809423507429663399 ,3.3852409662173708663363193655977056489010237256836 ],[1.6754996992362284602243821628316362157143541045237e1 ,1.6754996992362285656515428399018289240610660698131e1 ],[-2.6486582176162888682957875359465996103577202672261e-2 ,-2.6486582176162573801621144748408293199165971332124e-2 ]}
}
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={[-4.5743942211188589604334436070873164189351595682803e-16 ,4.5743942211188590918286855847004922003548981082959e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-2.5948721047412741355537492636263655291619482548262e-16 ,2.5948721047412736383054083314271714106474325360755e-16 ],[0 ,0 ]}
DH[2]=[-3.9599374921278811480764079314799069856647891339681e-2 ,-3.9599374921278811480764075338321672823284201432297e-2 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[-3.9599374921278927444555508565454213629823105259128e-2 ,-3.9599374921278695516972646087688723376324462327562e-2 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[1.0238282113101434690730733829900871018794287632905e1 ,1.0238282113101434690730736256754066503126224812487e1 ]
_H(5,0,0)=[-9.2176646874225566171777171812785870587603665849359e-15 ,9.2176643305185207804677331054180996552599944741724e-15 ]
_H(5,0,2)=[-2.8289584183557678694381159602590294697752068939429e2 ,-2.8289584183557668605134088304474206098961512721565e2 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-3.2583245577642678234403735223493294349243792027429e-17 ,3.2583244316033339896557212919555272042304753101621e-17 ],[0 ,0 ],[-1.3549491177818953473298905356771946204433134650789e-16 ,1.3549491702449479317311698244379364227669558729347e-16 ],[0 ,0 ]}
DH*T2=[-3.6906726454894877849186756705205420316763141816908e-4 ,-3.6906726454882526998394712962424621898717209892417e-4 ]
Is Jacobi integral monotone along bifurcation curve:
!isSingular(DH*T2): true
############################

Bound on Jacobi constant: [3.0058996184784557877300047864824864203177634971557 ,3.0058996184784557877300047874711154203837541756950 ]
dat/JupiterL1_04_PT.dat at {9.5024214388859370577645905233401410860214480973371e-1 ,0 ,8.1676422659915674194420062246092845856184813324511e-2 ,0 ,1.0010076870391574821367119426714994541793583524600e-1 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 10:55:50 2018
elapsed time: 0hours 19minutes 54seconds