Started: Thu Nov 29 10:35:56 2018

Available threads: 0

Problem: dat/JupiterL1_05_PT.dat at {9.5376936410451937638712875736139463284658631274833e-1 ,0 ,8.2719017380738086552782853935429753924857857219188e-2 ,0 ,9.5394019806602832632464820692045333193688385974009e-2 ,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]=[-9.5445892018282761137943647107014663392741569216237e-34 ,9.5445850494339911488618402464395712842960698350561e-34 ]
D0[i][3][0]=[-6.6142076523518340817775066911623918076911638664335 ,-6.6142076523518340817775066911542085049963992876576 ]
D0[i][3][2]=[-2.1957889482532977895656455312638984624902114229674e-30 ,2.1957898271110052619990656639936637376853376250327e-30 ]
dy0=[-1.4328207020429090432560503991804105533259577670619e-32 ,8.5030303965398566907926449486018140737935522556302e-33 ]
Ddy=[-6.9457552310802081308504630488895363570052472854885 ,-6.9457552310802023159476492214239131023937888723930 ]
dy=[-2.0628724370122629340906512808657051406425739452098e-33 ,1.2242053043406004512843352225518945962475487858148e-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]=[-1.7370838322111174728582058340956725447476781066994e-31 ,1.7370838327499607382686399201101997573409402794894e-31 ]
D0[i][3][0]=[-1.9789378388816234980656026016486569853604163303027 ,-1.9789378388816234980656025996110004926828595059819 ]
D0[i][3][2]=[-5.4973484920321557465958180324629954574667555992415e-28 ,5.4973484975673998004894162037902740455744754335616e-28 ]
dy0=[-1.8275760614438059116443992044376611756120095292943e-31 ,1.7596687821966615686123435659458766456541772832611e-31 ]
Ddy=[-9.1710297535415829249374225760409856268660739383094 ,-9.1710297535415744579347305714271858630845116556868 ]
dy=[-1.9927708344180775150960172642649518755873442242478e-32 ,1.9187254097797803766863820481687045044260738083193e-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]=[-1.7064866868708539419754216332424420703241003030294e-29 ,1.7064866867366781272394896920929439300803010748770e-29 ]
D0[i][3][0]=[-1.1921371800320323580923178943683651639340894203194e-25 ,1.1921371800709636993237582208120136574977604171855e-25 ]
D0[i][3][2]=[-9.2121897711151456441746318788939470290811015849969e-26 ,9.2121897714290557378422301291879565622153133428047e-26 ]
dy0=[-1.7064866868709460644638926219950262198928015749163e-29 ,1.7071873958172501660648976285906075888289350716069e-29 ]
Ddy=[9.8458547091663958359269008747745521669521907815285 ,9.8458547091680105960196515820602887361786949055302 ]
dy=[-1.7339148771186671636721108203724429568987312625837e-30 ,1.7332031979734815777770533912715348154163514949397e-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]=[-6.9457552310802052233990561352907447505240327065988 ,-6.9457552310802052233990561350227047088750034512828 ]
D0[i][5][0]=[1.9016503432639125366282910189192772708883848649861 ,1.9016503432639125366282910189439286471483548847007 ]
D0[i][3][0]=[-6.6142076523518340817775066911623918076911638664335 ,-6.6142076523518340817775066911542085049963992876576 ]
DBif[i][5][0]=[1.9016503432639125366282910183236618075901425177068 ,1.9016503432639125366282910195395441104465972319801 ]
DBif[i][3][0]=[-6.6142076523518340817775066917289610031746447523194 ,-6.6142076523518340817775066905876393095129184017716 ]
D[k][3][4]=[-6.9457552310802073727361891713970257696017536953317 ,-6.9457552310802030740619230989164236897972824625499 ]
_H(5,0,0)=[3.0071239645756273798834422117404145889443759653325e1 ,3.0071239663926315292338649933020986950465358274074e1 ]
_H(5,0,2)=[-8.0288290608386824081714051747405243097239221144266 ,-8.0288290454685181665130834875924015927033332710259 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[-9.1710297535415786914360765746751740554701320274825 ,-9.1710297535415786914360765727929974344804535665136 ]
D0[i][5][0]=[5.5167977403161472852958525282110366697963637589036 ,5.5167977403161472852958525297425591897249311937044 ]
D0[i][3][0]=[-1.9789378388816234980656026016486569853604163303027 ,-1.9789378388816234980656025996110004926828595059819 ]
DBif[i][5][0]=[5.5167977403161472852958525274075998658307391995756 ,5.5167977403161472852958525305459959936905557530324 ]
DBif[i][3][0]=[-1.9789378388816234980656026023504387185514422636076 ,-1.9789378388816234980656025989092187594918335726770 ]
D[k][3][4]=[-9.1710297535415800863488947171510524602149716797127 ,-9.1710297535415772965232584303171190297356139142834 ]
_H(5,0,0)=[1.5054618364035649692345343273049104649128098058768e2 ,1.5054618549575014071132337245243111531126886839686e2 ]
_H(5,0,2)=[6.7145743263242405337621937101410819547290682510426e1 ,6.7145745171352346054096445382523153601109566973093e1 ]
Dg!=0.: true
############################

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

DBif[i][3][4]=[9.8458547091672032159732756529252588512639915145453 ,9.8458547091672032159732768039095820518668941725134 ]
D0[i][5][0]=[-3.7488327596352755758808138413040487054254550871835e-25 ,3.7488327596427730473145123633494212735509022835870e-25 ]
D0[i][3][0]=[-1.1921371800320323580923178943683651639340894203194e-25 ,1.1921371800709636993237582208120136574977604171855e-25 ]
DBif[i][5][0]=[-3.8110332286125460311013396874617881922090389791038e-25 ,3.8110332286200435025350382095071607603344861755073e-25 ]
DBif[i][3][0]=[-1.2435579709864085331731507475658156610929351670551e-25 ,1.2435579710253398744045910740094641546566061639212e-25 ]
D[k][3][4]=[9.8458547091671733296776632944527380059582964971945 ,9.8458547091672331022688891623821028971725891898642 ]
_H(5,0,0)=[-2.3745087474289113003024307458346188389727320155456e-4 ,2.3745087474356609698254393306235086062454121817154e-4 ]
_H(5,0,2)=[5.2403127518967850356882240240058312114537961675916e2 ,5.2403189056533046033093228466979994673365008113629e2 ]
g=[-5.2736073931026361646659051368490322404956274525475e-25 ,5.2736073931559220090228692118839961943312054423410e-25 ]
Dg=[5.2403127518967850356878862926103075914046844656536e2 ,5.2403189056533046033096605780935230873748981546493e2 ]
r[2]=[-9.9999999999999999999713588617421762351887558342849e-18 ,9.9999999999999999999713588617421762351887558342849e-18 ]
Dg!=0.: true
############################

-g/Dg=[-1.0063535599563376510087982597278960107895038656118e-27 ,1.0063535599461692036508277423670408875948771935937e-27 ]
Check existence of period-n branch:
subset(-g/Dg,r[2]): true
############################

D1={
{[-7.0572722079962849978765320024943768993790501266919e-1 ,-7.0572722079962849084665273154193126494503866276936e-1 ],[-2.3797935974904163843715269839394071530357249299211e-1 ,-2.3797935974904163263668473887892444093052735134226e-1 ],[1.5478456877252166078412162290201743782242088241511e-1 ,1.5478456877252166586844530175249235853352865135333e-1 ],[5.0673713266837020547777173493096603790801444011030e-1 ,5.0673713266837021148846457015249541079602102640154e-1 ],[-4.7898065505594483389360867953353770371110932226054 ,-4.7898065505594483351448599097193130830298486585113 ],[1.8177234936047306181486620226747186071904616762919e-1 ,1.8177234936047306446811405738062508683873255542540e-1 ]},
{[-4.2988446655477230479112486113931129694710467097970e-20 ,4.2988446655477230479110529428969789189342915429090e-20 ],[-1.8733772545499357906264670827844255533019287950164e-20 ,1.8733772545499357906264501318712008630554338387966e-20 ],[-1.3780365174118856084937401219400383162512255372441e-20 ,1.3780365174118856084937750921790265571724071590052e-20 ],[-4.1718217772745774127868636702772004244046231331716e-20 ,4.1718217772745774127869579163949550115917881619773e-20 ],[-1.8570163047281571954924277843560300421000225048119e-19 ,1.8570163047281571954923317821844346450618204132578e-19 ],[-1.8221823556497565531991936240935348443806115387050e-20 ,1.8221823556497565531992412887165472304506030602286e-20 ]},
{[-3.0668503506007382367964134676533176597639491688757e-1 ,-3.0668503506007380326989154605736985702976579787877e-1 ],[-8.2772572146584891539876072252059050200369553663245e-1 ,-8.2772572146584890216333084457131255473585170241957e-1 ],[5.0775767817087740287385660000289816284595063537811e-1 ,5.0775767817087741448130889551952360382341199493823e-1 ],[1.7625030976374472900392817061167485920969074515739 ,1.7625030976374473037457744372149471876332107599036 ],[-1.2068406267451714874604325599924101653291354018447e1 ,-1.2068406267451714865932090978827213524044533784380e1 ],[6.3222982520670392534384828653241854607758342622928e-1 ,6.3222982520670393141033436254580308372855355726130e-1 ]},
{[-4.6723588937002370097002855670608700427140158122809e-17 ,4.6723588271335199899134696538348717471515325927260e-17 ],[2.6828424315506531723817699249183330796732736384534 ,2.6828424315506532329034750502392675164489811698522 ],[-2.6598649077368552486402847786703435115169048038779e-17 ,2.6598649178842033619505013526306161674099450353540e-17 ],[-6.8146613598431111245065660915520777693748565341870e-1 ,-6.8146613598431104998219662432785980082822904154047e-1 ],[9.8458547091672031956090289611860927624233406488978 ,9.8458547091672032363375206380912614767428477568636 ],[9.5447191972535088192314310025988522546538991332831e-1 ,9.5447191972535091011449668440786687279384641635348e-1 ]},
{[2.6783132662277604889606657398214485920310915306496 ,2.6783132662277606582220376346561463075472652847342 ],[6.9488277204552074801569703903761435143290322070876 ,6.9488277204552075898323528999219024078169052315152 ],[-4.2376449008817703718097043007276148550781799444991 ,-4.2376449008817702756505848032643873591544467153295 ],[-1.4796363172769395414629961969168115998175518874843e1 ,-1.4796363172769395300849547779667207452091846743459e1 ],[1.0072843110616951095140416596188545415297471631740e2 ,1.0072843110616951102484617467234903577244328159545e2 ],[-5.3076230702541432477265106614922020978010500824507 ,-5.3076230702541431973749815445993054043311992972190 ]},
{[-1.6464828894139384740868374140795418651759564333658e-17 ,1.6464828773348505240297408584477890555923693162873e-17 ],[-8.9816075242016573817012628497819592524122642834742e-1 ,-8.9816075242016571707557322957037868428468999097278e-1 ],[-9.2432559521810261419810270281681713849695437979550e-18 ,9.2432559378291338608029381444978027012339584502769e-18 ],[4.6596365424173793096013938443155822127250826852283e-1 ,4.6596365424173795325048198075217227292399819327529e-1 ],[-1.1580018897667944451811111966800181207539042327481e1 ,-1.1580018897667944433553681197199113224175544756474e1 ],[-1.7755540123993198759076521093242205843774182928067e-1 ,-1.7755540123993197755079023150711649028423233708046e-1 ]}
}
D[2]={
{[-7.0572722079962850281849992489046069368927587454419e-1 ,-7.0572722079962848781580603323829384029550037686269e-1 ],[-2.3797935974904164346049369767364485577893415618157e-1 ,-2.3797935974904162761334371657080625115573820494723e-1 ],[1.5478456877252165702287036635543648681463182864972e-1 ,1.5478456877252166962969654226084603847308549783583e-1 ],[5.0673713266837019807198390381520824250734132852407e-1 ,5.0673713266837021889425237100448433369620076068302e-1 ],[-4.7898065505594483519154112579636428402200165206737 ,-4.7898065505594483221655353635035979929399569159915 ],[1.8177234936047306082579008473290608527530681685701e-1 ,1.8177234936047306545719017225324054786471391701676e-1 ]},
{[-1.0708995761628439107640295050831150141563628299011e-16 ,1.0708995761628439107682501722464712601804285681195e-16 ],[-7.3914398478825588037177580024586145919934621032392e-17 ,7.3914398478825588036886265991503206960583425893360e-17 ],[-6.3634838417777842188444381490833518905987549345288e-17 ,6.3634838417777842188695181359405466347597892993370e-17 ],[-8.0242156067204919738632939945651748701190612077539e-17 ,8.0242156067204919738949193160022485425410285364030e-17 ],[-7.4054623084319768789340556007680143237246586931460e-17 ,7.4054623084319768789048689316438514451753799061956e-17 ],[-3.0660470904968457582130116271299188552441661491262e-17 ,3.0660470904968457582250956400142382579596153800844e-17 ]},
{[-3.0668503506007383008569645049761825023956236208009e-1 ,-3.0668503506007379686383622451098978584803595316191e-1 ],[-8.2772572146584892422704358177731830140464348904832e-1 ,-8.2772572146584889333504813306232736631922230324551e-1 ],[5.0775767817087739610500966307013060435903741337040e-1 ,5.0775767817087742125015593610844271857422489134763e-1 ],[1.7625030976374472769529587691349783840254518766042 ,1.7625030976374473168320975545961274844627589045406 ],[-1.2068406267451714897285649541350761025910414746519e1 ,-1.2068406267451714843250767346965523362593739459710e1 ],[6.3222982520670392335909855115702633619871309788259e-1 ,6.3222982520670393339508410402721098639753641755998e-1 ]},
{[-2.4472015138677651867108180621222441320534847132402e-16 ,2.4472015222602098434356940792516599550025159578616e-16 ],[2.6828424315506530207186828310085259597972962848150 ,2.6828424315506533845665611457320207370236339564194 ],[-1.5358305727204174550540985972377356092515612900060e-16 ,1.5358305807280806561990370735512159524369036088827e-16 ],[-6.8146613598431128948668215622202913769910383829760e-1 ,-6.8146613598431087294616986990633512449120413057980e-1 ],[9.8458547091672029590818877378201038686293182816347 ,9.8458547091672034728646599100561210512408577739059 ],[9.5447191972535082674076609501954460116845063744641e-1 ,9.5447191972535096529687372256085554431363591468566e-1 ]},
{[2.6783132662277604271504085787647354496814777373361 ,2.6783132662277607200322929155033098925714778619698 ],[6.9488277204552073929397601909955981039174804541423 ,6.9488277204552076770495644112324973637927774012924 ],[-4.2376449008817704382878580479687392565297659297733 ,-4.2376449008817702091724319745139783173499762297042 ],[-1.4796363172769395545093850706172455716015239187309e1 ,-1.4796363172769395170385660670606075729626693046869e1 ],[1.0072843110616951050332528517795461869796031655485e2 ,1.0072843110616951147292505856244804939081801415412e2 ],[-5.3076230702541432663784793656632219838247095117126 ,-5.3076230702541431787230129151323999478171675576195 ]},
{[-9.9127040555457948614172533501692290819506014909167e-16 ,9.9127040560028528165475758976303900211247324930910e-16 ],[-8.9816075242016643520325421733672112491977029389398e-1 ,-8.9816075242016502004244540486096171061622908381033e-1 ],[-6.0515416872038741487537599264491398176970565176314e-16 ,6.0515416878320220593955119822295611600920270346766e-16 ],[4.6596365424173715506916015289745235384207839084552e-1 ,4.6596365424173872914146134712973245333678534755003e-1 ],[-1.1580018897667945242404567507019050940153528257730e1 ,-1.1580018897667943642960225882161129003432429667044e1 ],[-1.7755540123993226879026667912819622178396326092186e-1 ,-1.7755540123993169635128875720591903241138828847171e-1 ]}
}
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={[-1.4223211259522686820329675371807940815007249770544e-16 ,1.4223211259522686369105452126029052502433008221678e-16 ],[0 ,0 ],[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-1.4233580825765507914128915902897262702602587072001e-16 ,1.4233580825765511226476617745885475379322059285613e-16 ],[0 ,0 ]}
DH[2]=[1.5404882178190610992912647006503839804115798852783e-2 ,1.5404882178190610992912665127739355937668679735647e-2 ]
Is Jacobi integral monotone along space-parameter of fixed point curve:
!isSingular(DH[2]): true
############################

DH*T1=[1.5404882178190545305588031693512997154620144560861e-2 ,1.5404882178190676680237280440715255700652802082455e-2 ]
Is Jacobi integral monotone along fixed point curve:
!isSingular(DH*T1): true
############################

D[k][3][4]=[9.8458547091672032159732726453073790658958712468949 ,9.8458547091672032159732798115274618068452932692419 ]
_H(5,0,0)=[-2.6118838969373282316971306857839887705588607535995e-13 ,2.6118839268888461210520752621877211599970701149095e-13 ]
_H(5,0,2)=[5.2403158287750420343660612673898311105579711602613e2 ,5.2403158287750476063788745835068389224257219481455e2 ]
T2={[1.0000000000000000000000000000000000000000000000000 ,1.0000000000000000000000000000000000000000000000000 ],[0 ,0 ],[-4.9842108991728290647439862106181724800847721903269e-16 ,4.9842108420168887206744818785093445809686453267396e-16 ],[0 ,0 ],[-2.1121315660247883224728313892261108384083362747381e-15 ,2.1121315902454462378878500779380390412860405604198e-15 ],[0 ,0 ]}
DH*T2=[1.2014041977756288235845849614867404672210813375242e-2 ,1.2014041977758202356709631300851566089756816302711e-2 ]
Is Jacobi integral monotone along bifurcation curve:
!isSingular(DH*T2): true
############################

Bound on Jacobi constant: [3.0058451498895476042688659608096019467177148659730 ,3.0058451498895476042688659659861329885091536833336 ]
dat/JupiterL1_05_PT.dat at {9.5376936410451937638712875736139463284658631274833e-1 ,0 ,8.2719017380738086552782853935429753924857857219188e-2 ,0 ,9.5394019806602832632464820692045333193688385974009e-2 ,0 } completed.
Final result: true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


Finished: Thu Nov 29 10:56:15 2018
elapsed time: 0hours 20minutes 19seconds