Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL1_09_PT.dat at {-9.3400922761599767510013878695986761805778128100545e-1 ,0 ,4.5713486736248961862905244564481676255114349412289e-2 ,0 ,2.0032253778932114594087358864859349980391066045584 ,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]=[-6.5262514446861906045746194833222997073090837202695e-33 ,6.5262514261731662274783592144513977183839121792877e-33 ]
D0[i][3][0]=[7.0911899852622031725915562904769948472405422947690e-1 ,7.0911899852622031725915562907351357357730896357562e-1 ]
D0[i][3][2]=[-6.2449317383419904803445023198018702035381537227645e-30 ,6.2449317421182892649514240807651081357193671471710e-30 ]
dy0=[-1.3415235470345259415969975715925275853213691109571e-32 ,1.4621777095590957916204512523049831938711192378747e-32 ]
Ddy=[1.1895351341153668315563997666892894694521374654930e1 ,1.1895351341153806868110919650458702100096053710377e1 ]
dy=[-1.2292009438178450417976896092496733318308128080599e-33 ,1.1277712684225925046437014569913631875514745775518e-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]=[-7.8258786417558351272960523210793039383630839433883e-31 ,7.8258786397195218341135576777092336878839179387895e-31 ]
D0[i][3][0]=[1.3913813020926394352004513085688686216554025474923e-2 ,1.3913813020926394352004514180873600779156531660159e-2 ]
D0[i][3][2]=[-2.6663005482900330687627692322420468942712412284194e-28 ,2.6663005483563752285443250093502857316594370149107e-28 ]
dy0=[-7.8272303476872552515313115579088445546816271609303e-31 ,7.8304799835332118740562215588219883440986955709505e-31 ]
Ddy=[4.5669635105926505775671357535215381041084516085775 ,4.5669635105927692916753984019881657945982817418369 ]
dy=[-1.7145921935594921843925760414578456411557928395105e-31 ,1.7138806407217216631377136904680871353523714279317e-31 ]
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]=[-2.4313591577342562763767700416486651443137628873663e-28 ,2.4313591577534363817763615915293928117092833642654e-28 ]
D0[i][3][0]=[-2.0786864563925069973898690907956264293160952400797e-25 ,2.0786864563924662332689136218964326926161845079080e-25 ]
D0[i][3][2]=[-5.3569465900498023486555469910815492900782646722680e-25 ,5.3569465900479394404584267009000631757898969247194e-25 ]
dy0=[-2.4314910126911433844452884802082966064330428292534e-28 ,2.4313591577534899512527096770431825572275915424428e-28 ]
Ddy=[-1.8965174431259636346922149684453488409130365418265e2 ,-1.8965174431258577046862878606028251424555541584053e2 ]
dy=[-1.2820820718018481613664058271927906755390654034061e-30 ,1.2820125470325762749676792536106994581597710178119e-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]=[1.1895351341153737591837458650622346432016450188031e1 ,1.1895351341153737591837458666729250362600978177276e1 ]
D0[i][5][0]=[7.6509924472716932495735659279709396770693874596755e-1 ,7.6509924472716932495735659281267810434859236650849e-1 ]
D0[i][3][0]=[7.0911899852622031725915562904769948472405422947690e-1 ,7.0911899852622031725915562907351357357730896357562e-1 ]
DBif[i][5][0]=[7.6509924472716932495735659268651130523504364906165e-1 ,7.6509924472716932495735659292326076682048746341439e-1 ]
DBif[i][3][0]=[7.0911899852622031725915562903389917258103458348708e-1 ,7.0911899852622031725915562908731388572032860956545e-1 ]
D[k][3][4]=[1.1895351341153730950638727440846770359308587112312e1 ,1.1895351341153744233036189876504826435308841252995e1 ]
_H(5,0,0)=[4.5446615022776569849329875369825078662209817706688e1 ,4.5446615033302740802922965904068360375353004896666e1 ]
_H(5,0,2)=[1.7672241000463896569753783145269459347802148687863e2 ,1.7672241001372053384651076118724965996989878022916e2 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[4.5669635105927099346212670689004775925805344539290 ,4.5669635105927099346212670866092263061261988964854 ]
D0[i][5][0]=[-3.1209633810673866828752202872828393278677873061081e-2 ,-3.1209633810673866828752202840667038257902604444786e-2 ]
D0[i][3][0]=[1.3913813020926394352004513085688686216554025474923e-2 ,1.3913813020926394352004514180873600779156531660159e-2 ]
DBif[i][5][0]=[-3.1209633810673866828752202883130208952991789866054e-2 ,-3.1209633810673866828752202830365222583588687639813e-2 ]
DBif[i][3][0]=[1.3913813020926394352004513024300845719268140327587e-2 ,1.3913813020926394352004514242261441276442416807495e-2 ]
D[k][3][4]=[4.5669635105927098187884404191642339561044412854886 ,4.5669635105927100504540937363454699426022920649258 ]
_H(5,0,0)=[5.7058332796610891582349465547906534034054101520591e-1 ,5.7058375644174191499965292830123615546914263772255e-1 ]
_H(5,0,2)=[3.1928404635328042821507575049160706215231402828876 ,3.1928408576561689014431732023696895660082504038937 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-1.8965174431259106696892516507164578155644580843918e2 ,-1.8965174431259106696892511783317161678041326158400e2 ]
D0[i][5][0]=[-1.2525131923983136182138396960981877944660678915239e-25 ,1.2525131923959953650729030260037988390156091794305e-25 ]
D0[i][3][0]=[-2.0786864563925069973898690907956264293160952400797e-25 ,2.0786864563924662332689136218964326926161845079080e-25 ]
DBif[i][5][0]=[-1.3216295156738010193906540774472698803508398054648e-25 ,1.3216295156714827662497174073528809249003810933714e-25 ]
DBif[i][3][0]=[-2.0871665465947688388579978097554520042955526020253e-25 ,2.0871665465947280747370423408562582675956418698536e-25 ]
D[k][3][4]=[-1.8965174431259108252373711459140405609568253168606e2 ,-1.8965174431259105141411316831341334224117653833711e2 ]
_H(5,0,0)=[-1.6359340902625467974769309542801329422078571482095e-5 ,1.6359340902659174044972723908498228944334016220868e-5 ]
_H(5,0,2)=[-9.6281165879289963625179310770858776235688898501649e1 ,-9.6281131034734474175842674250391170048883122140728e1 ]
g=[-2.3415002593887970971053409388938995762296756985929e-25 ,2.3415002593864589247667955784562071625694428909906e-25 ]
Dg=[-9.6281165879289963625185291190422298193833800516579e1 ,-9.6281131034734474175836693830827648091481379394779e1 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-2.4319409568880897270135429018359776004007348346451e-27 ,2.4319409568856612425187961179432952493828226703678e-27 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

D1={
{[-3.4260761684956429580060301281967910429077272928402e-2 ,-3.4260761684956416481010854401500940636053965665271e-2 ],[-9.5117344534183487526609192248041798680819715092523 ,-9.5117344534183487060105526066979911262500881529067 ],[-4.9635653912380551066920677330327983522546438389976e-2 ,-4.9635653912380544752386880001997915267759140060730e-2 ],[4.5462845037601454406572811364175005411987002386609 ,4.5462845037601454667561488669154023828476123468973 ],[-6.1977652497928399499267742383559926493839784193721 ,-6.1977652497928399197510240256046065394661873210462 ],[2.0268149542856811729742824297388052691378762410493 ,2.0268149542856811830427559493049592502118412285848 ]},
{[-3.0234139390970794364842055307918272509024749497298e-21 ,3.0234139390970794364841744917117009033375952673618e-21 ],[-1.5455185887664770532841501253955832410407326470974e-19 ,1.5455185887664770532841458085609414350843674487125e-19 ],[-2.6251193394856533194178733702199671514410804163144e-21 ,2.6251193394856533194178532809934183894655890419926e-21 ],[-7.4229910528895831382721849539095288550360159109871e-20 ,7.4229910528895831382722072434017110100109005635433e-20 ],[-1.6476056907869616504431702283905877658175243185981e-19 ,1.6476056907869616504431622308643953558186596864113e-19 ],[-9.9839538314213646312683586612283612706917057213643e-20 ,9.9839538314213646312684925151986434924666678793256e-20 ]},
{[-5.2035047526267777667684407082342580031349643532699e-2 ,-5.2035047526267777199536262831798399423914996832273e-2 ],[8.8157865222577523713991719417858678435114296460687 ,8.8157865222577523731472565785401869022691613308875 ],[-4.5279550568248241688260108189955565616570728434026e-2 ,-4.5279550568248241462191792590811653765851858397228e-2 ],[-4.2136451402082882708245030838279805142354645944590 ,-4.2136451402082882698541871505371966706173861240733 ],[9.2425463338953140182268512859966602358405084233186 ,9.2425463338953140193923335293055147562460202605074 ],[-1.8785183758657959304208313932675929795611867218255 ,-1.8785183758657959300159099847320163918921242608248 ]},
{[-3.5352841531510339226691385478767619872656575269943e-17 ,3.5352841675485762174490826895828347084648164803763e-17 ],[-1.9659802119124890396696470614047496867627805137399e2 ,-1.9659802119124890368759587805114205807813642012298e2 ],[-1.7162246567698719204018964614094667436542442333201e-17 ,1.7162246487163994904842932661242254207135012521124e-17 ],[9.4270877410690696999816344674246163372575118820700e1 ,9.4270877410690697153780400747494753706065589876584e1 ],[-1.8965174431259106706530343198400922091178229354628e2 ,-1.8965174431259106687254685206471063273884580796492e2 ],[6.4748800719543346788151399095277539765390309028750e1 ,6.4748800719543346861496103798902969135524806967970e1 ]},
{[3.6378020742156539531631925749748009186480387408190e-2 ,3.6378020742156714261796693277274419901204728929369e-2 ],[-2.0530041417122879298090360905505627171220137537698e2 ,-2.0530041417122879232951673749189053051265199093230e2 ],[-2.0184180411143417819860783454279283102141531603843e-1 ,-2.0184180411143409373365967902717491476816415612802e-1 ],[9.8126592592875246865935254882076489918222485216487e1 ,9.8126592592875247227862098436732653738045316734242e1 ],[-1.6662613307672095435079541613811367483070873300620e2 ,-1.6662613307672095391659036455183712393226668102696e2 ],[4.3746590235574690145134306083219693892593064540272e1 ,4.3746590235574690298402154112942787708980862830442e1 ]},
{[-9.8382452011732800130698924443499416834223596760190e-17 ,9.8382451460191759403099168710388724731943421986619e-17 ],[1.4468642874363188632138415372500470118537699592921e2 ,1.4468642874363188703683506720933097104761184411186e2 ],[-4.7486678787306838868358722293779414615708539887696e-17 ,4.7486679085789420015760532426331620925277428621055e-17 ],[-6.8827466544044814749249426498214502566363198390316e1 ,-6.8827466544044814350241442525304308021411344917230e1 ],[9.2672440451300843093392222206098137212313574303743e1 ,9.2672440451300843562589249046545359486992692401425e1 ],[-6.1696736539370392423498021649629504970446530813917 ,-6.1696736539370390814128223651387772308688159219562 ]}
}
D[2]={
{[-3.4260761684956424441146625145751500121317621163899e-2 ,-3.4260761684956421619924530501668694979842742646935e-2 ],[-9.5117344534183487473114724739880537221524486610490 ,-9.5117344534183487113599993640365749488419433669369 ],[-4.9635653912380548928432342548077267260743400212252e-2 ,-4.9635653912380546890875215016856722425307243032657e-2 ],[4.5462845037601454444349397684309692614272741270065 ,4.5462845037601454629784902382397155721127073150901 ],[-6.1977652497928399532251727969974225589120423948523 ,-6.1977652497928399164526254775938872354295264401163 ],[2.0268149542856811629293542601014612559531172599407 ,2.0268149542856811930876841308558526323799477726496 ]},
{[-7.7453747512023170539094476446775496570538391803835e-18 ,7.7453747512023170538541591402825494119560870827859e-18 ],[-4.8914474660508616947480579063561031746058219038267e-17 ,4.8914474660508616947131414790156849123476376106705e-17 ],[-4.2668883432613909681354317618831617161784187541948e-18 ,4.2668883432613909681049736004000440191298117482211e-18 ],[-2.6163667744264537280581628759418985561079411130181e-17 ,2.6163667744264537280768391841327133075791685387463e-17 ],[-4.2815568622918071656197453861137752922813800481071e-17 ,4.2815568622918071655891825169173535464132978600371e-17 ],[-3.5104814138265366648029265291864011420286800597524e-17 ,3.5104814138265366648279852607922264904035989775700e-17 ]},
{[-5.2035047526267777775064358377325114752018155055434e-2 ,-5.2035047526267777092156311541338183320863955278616e-2 ],[8.8157865222577523673753673562227455209263402696532 ,8.8157865222577523771710611707271329590741936400850 ],[-4.5279550568248241832080100852885869225589153306897e-2 ,-4.5279550568248241318371799885836084276002892946987e-2 ],[-4.2136451402082882728536933239950506068130781026204 ,-4.2136451402082882678249969135624052968006261112279 ],[9.2425463338953140135128620488118782703532644754195 ,9.2425463338953140241063227718748414102177612112616 ],[-1.8785183758657959354552657623573776020383076475522 ,-1.8785183758657959249814756180183907605621447008734 ]},
{[-1.4838972472396667169973741464502987200122632089378e-16 ,1.4838972490455259258435617351673936869660784678644e-16 ],[-1.9659802119124890650462559000677616557774863752173e2 ,-1.9659802119124890114993499759992091031413796169497e2 ],[-1.2146862484923701466254172900797631091464072734961e-16 ,1.2146862480072820732856416141982254611207262163007e-16 ],[9.4270877410690695713196715197591770141065453608505e1 ,9.4270877410690698440400031859658732978276603191059e1 ],[-1.8965174431259106982870055044987510547883534228449e2 ,-1.8965174431259106410914973793999251578044729528908e2 ],[6.4748800719543343941668871700089060300457257007710e1 ,6.4748800719543349707978632080679848531847644308953e1 ]},
{[3.6378020742156530162672024078010232486348879469719e-2 ,3.6378020742156723630756607378622018396659502669533e-2 ],[-2.0530041417122879610139843668810378571899477209006e2 ,-2.0530041417122878920902191641529396672443765607711e2 ],[-2.0184180411143426190169495268642121871837646281902e-1 ,-2.0184180411143401003057255832477994056042284766569e-1 ],[9.8126592592875245307156611289017948757819163818017e1 ,9.8126592592875248786640745165660210718315568280132e1 ],[-1.6662613307672095816331884305598295802138738965679e2 ,-1.6662613307672095010406694345387716644819004080009e2 ],[4.3746590235574685688814050365040814906972946594862e1 ,4.3746590235574694754722411332419978140315254560976e1 ]},
{[-1.0250878235832242796281875490214356229402497517093e-16 ,1.0250878181815251239359534291313339051980102817995e-16 ],[1.4468642874363188480780077798656168085805444375318e2 ,1.4468642874363188855041844986835944119069579736130e2 ],[-8.3767538123336182170347883622836904337748371523527e-17 ,8.3767538446934630971665406972471850647068289966735e-17 ],[-6.8827466544044815502260957248272528028659297818794e1 ,-6.8827466544044813597229915085997369405759909721401e1 ],[9.2672440451300841322771471364719328118066652561444e1 ,9.2672440451300845333210005006127941313231009684553e1 ],[-6.1696736539370411426756250300268016015732389906980 ,-6.1696736539370371810870011130906343836016951486059 ]}
}
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={[-3.6556604566812678893059919679484711013389603855412e-16 ,3.6556604566812674350338587554194002174421633851206e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.3904955462975811019132501875454993158296001746682e-17 ,1.3904955462975810527289670736687553545706293630463e-17 ],[0 ,0 ]}
DH[2]=[1.5555096725649042056444829174648346558257611367573e-1 ,1.5555096725649042056444831210057227661409343086259e-1 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[1.5555096725649034653005112522523226169450833483674e-1 ,1.5555096725649049459884547862182318419938239911093e-1 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[-1.8965174431259106696892516885448404361760735592914e2 ,-1.8965174431259106696892511405033335472302917589523e2 ]
_H(5,0,0)=[-6.3493234359424270788751167093691321299691769272411e-13 ,6.3493234247466080319748949081625451998556270521773e-13 ]
_H(5,0,2)=[-9.6281148457012807671928743867851629555512045220598e1 ,-9.6281148457011630158835936678399058287287564402990e1 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-6.5945655382136652658026390097710324568055518531522e-15 ,6.5945655265854086170994717688538197814198486828253e-15 ],[0 ,0 ],[-1.3310590032183072548587721340602199537534574633978e-15 ,1.3310590055653755555037990102247883515634901135622e-15 ],[0 ,0 ]}
DH*T2=[4.9950883368807550613183089266007729494799822886803e-2 ,4.9950883368820280194499020589160489703928789297554e-2 ]
Is Jacobi integral monotone along bifurcation curve:
!isSingular(DH*T2): true
############################

Bound on Jacobi constant: [-1.0006666037342203004067305518706541550265454269880 ,-1.0006666037342203004067305431907077425562136884139 ]
dat/JupiterL1_09_PT.dat at {-9.3400922761599767510013878695986761805778128100545e-1 ,0 ,4.5713486736248961862905244564481676255114349412289e-2 ,0 ,2.0032253778932114594087358864859349980391066045584 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 11:19:56 2018
elapsed time: 0hours 44minutes 0seconds