{"id":"https://openalex.org/W7124148412","doi":"https://doi.org/10.1007/s00332-025-10238-4","title":"Simultaneous Computation of Whiskered Tori and Their Whiskers in Hamiltonian Systems Using Flow Maps","display_name":"Simultaneous Computation of Whiskered Tori and Their Whiskers in Hamiltonian Systems Using Flow Maps","publication_year":2026,"publication_date":"2026-01-14","ids":{"openalex":"https://openalex.org/W7124148412","doi":"https://doi.org/10.1007/s00332-025-10238-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-025-10238-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-025-10238-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-025-10238-4.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-025-10238-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"\u00c1lvaro Fern\u00e1ndez-Mora","orcid":"https://orcid.org/0000-0002-3863-0003"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"\u00c1lvaro Fern\u00e1ndez-Mora","raw_affiliation_strings":["Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-3863-0003","affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043146898","display_name":"\u00c0lex Haro","orcid":"https://orcid.org/0000-0002-7188-9172"},"institutions":[{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]},{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"\u00c0lex Haro","raw_affiliation_strings":["Centre de Recerca Matem\u00e0tica, Edifici C, Campus Bellaterra, 08193, Bellaterra, Spain","Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0003-0377-8099","affiliations":[{"raw_affiliation_string":"Centre de Recerca Matem\u00e0tica, Edifici C, Campus Bellaterra, 08193, Bellaterra, Spain","institution_ids":["https://openalex.org/I4210122226"]},{"raw_affiliation_string":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004732229","display_name":"Rafael de la Llave","orcid":"https://orcid.org/0000-0002-0286-6233"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rafael de la Llave","raw_affiliation_strings":["School of Mathematics (emeritus), Georgia Institute of Technology, 686 Cherry Street NW, 30332, Atlanta, GA, USA"],"raw_orcid":"https://orcid.org/0000-0002-0286-6233","affiliations":[{"raw_affiliation_string":"School of Mathematics (emeritus), Georgia Institute of Technology, 686 Cherry Street NW, 30332, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111526750","display_name":"Josep Mar\u00eda Mondelo","orcid":null},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]},{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Josep M. Mondelo","raw_affiliation_strings":["IEEC-CERES & Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Av.\u00a0de l\u2019Eix Central, Edifici C, Bellaterra, 08193, Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-7135-0599","affiliations":[{"raw_affiliation_string":"IEEC-CERES & Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Av.\u00a0de l\u2019Eix Central, Edifici C, Bellaterra, 08193, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942","https://openalex.org/I4210122226"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I71999127"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05079227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.6626999974250793,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.6626999974250793,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.2021999955177307,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.039000000804662704,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7843999862670898},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7516999840736389},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.6919999718666077},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6363000273704529},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6320000290870667},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5997999906539917},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5365999937057495}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7843999862670898},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7516999840736389},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.70660001039505},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.6919999718666077},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6363000273704529},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6320000290870667},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5997999906539917},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5365999937057495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49869999289512634},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4406999945640564},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C82229145","wikidata":"https://www.wikidata.org/wiki/Q2257676","display_name":"Standard map","level":3,"score":0.28130000829696655},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.26190000772476196},{"id":"https://openalex.org/C25902001","wikidata":"https://www.wikidata.org/wiki/Q1024820","display_name":"Flow map","level":3,"score":0.2567000091075897},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2538999915122986}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-025-10238-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-025-10238-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-025-10238-4.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00332-025-10238-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-025-10238-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-025-10238-4.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5054067969322205,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2092432181","display_name":null,"funder_award_id":"PID2021-125535NB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G3417140244","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G4387768949","display_name":null,"funder_award_id":"PID2020-118281GB-C31","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5805502524","display_name":null,"funder_award_id":"PID2020","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G6283739012","display_name":null,"funder_award_id":"PID2021-125535NB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6589649124","display_name":null,"funder_award_id":"PID2020-","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G84477964","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8613382760","display_name":"Stability and Transitions in Physical Processes","funder_award_id":"734557","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320323428","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7124148412.pdf"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W201746522","https://openalex.org/W605587302","https://openalex.org/W1585304689","https://openalex.org/W1928296088","https://openalex.org/W1973148663","https://openalex.org/W1993430945","https://openalex.org/W1996087276","https://openalex.org/W2001742524","https://openalex.org/W2005264856","https://openalex.org/W2008717493","https://openalex.org/W2013946715","https://openalex.org/W2021106480","https://openalex.org/W2021708781","https://openalex.org/W2027058059","https://openalex.org/W2067503369","https://openalex.org/W2068783610","https://openalex.org/W2072460339","https://openalex.org/W2074147617","https://openalex.org/W2080409870","https://openalex.org/W2088212036","https://openalex.org/W2106220517","https://openalex.org/W2167309987","https://openalex.org/W2275475826","https://openalex.org/W2326458513","https://openalex.org/W2389184278","https://openalex.org/W2476271725","https://openalex.org/W2613178133","https://openalex.org/W2613939086","https://openalex.org/W2963039554","https://openalex.org/W2963881724","https://openalex.org/W3089893562","https://openalex.org/W3104136855","https://openalex.org/W3119363060","https://openalex.org/W3124331571","https://openalex.org/W3172724430","https://openalex.org/W4212928962","https://openalex.org/W4213385762","https://openalex.org/W4231941367","https://openalex.org/W4234175586","https://openalex.org/W4235082200","https://openalex.org/W4242360818","https://openalex.org/W4247344744","https://openalex.org/W4285800550","https://openalex.org/W4296477255","https://openalex.org/W4381429221","https://openalex.org/W4384818516","https://openalex.org/W4390583356","https://openalex.org/W4390823277","https://openalex.org/W4394849304","https://openalex.org/W4406242552","https://openalex.org/W4410836490"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,64,91,229],"consider":[2],"autonomous":[3],"Hamiltonian":[4,189],"systems":[5],"and":[6,30,81,103,200,217,223,232],"present":[7,65,230],"an":[8],"algorithm":[9,195],"to":[10,39,78,134],"compute":[11,79],"at":[12],"the":[13,68,71,88,101,153,188,192,194,215,218,221,224,227,237],"same":[14],"time":[15],"partially":[16],"hyperbolic":[17],"invariant":[18,53,83],"tori":[19,35,80],"(whiskered":[20],"tori),":[21],"as":[22,24],"well":[23],"high-order":[25],"expansions":[26],"of":[27,99,124,137,155,157,178,191,214,226],"their":[28,52,82],"stable":[29],"unstable":[31],"manifolds.":[32],"Such":[33],"whiskered":[34],"have":[36],"been":[37],"shown":[38],"be":[40],"important":[41],"for":[42,96],"transport":[43],"phenomena":[44],"in":[45,60,66,116,121,236],"phase":[46,160],"space.":[47],"For":[48],"instance,":[49],"by":[50],"following":[51],"manifolds,":[54],"one":[55],"could":[56],"obtain":[57],"zero-cost":[58],"trajectories":[59],"space":[61,161],"mission":[62],"design.":[63],"detail":[67],"case":[69],"when":[70],"(un)stable":[72],"directions":[73],"are":[74,109,132],"one-dimensional.":[75],"The":[76,175,211],"strategy":[77],"manifolds":[84],"is":[85,113,152,162,181,208],"based":[86],"on":[87],"parameterization":[89,98],"method.":[90],"formulate":[92],"a":[93,97,122,128,169,201],"functional":[94],"equation":[95,112],"both":[100],"torus":[102,216],"its":[104],"whiskers":[105,219],"expressing":[106],"that":[107,172],"they":[108],"invariant.":[110],"This":[111],"naturally":[114],"discretized":[115],"Fourier-Taylor":[117],"series":[118],"or,":[119],"equivalently,":[120],"grid":[123],"Taylor":[125],"series.":[126],"Using":[127],"return":[129],"map,":[130],"we":[131,167],"reduced":[133],"study":[135],"functions":[136],"$$n":[138],"-":[139],"1$$":[140],"<mml:math":[141],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[142],"<mml:mrow>":[143],"<mml:mi>n</mml:mi>":[144],"<mml:mo>-</mml:mo>":[145],"<mml:mn>1</mml:mn>":[146],"</mml:mrow>":[147],"</mml:math>":[148],"variables":[149],"where":[150],"n":[151,164],"number":[154],"degrees":[156],"freedom":[158],"(the":[159],"2":[163],"dimensional).":[165],"Then,":[166],"implement":[168],"Newton-like":[170],"method":[171],"converges":[173],"quadratically.":[174],"key":[176],"advantage":[177],"our":[179],"approach":[180],"that,":[182],"using":[183],"geometric":[184],"identities":[185],"coming":[186],"from":[187],"nature":[190],"problem,":[193],"has":[196],"small":[197],"storage":[198],"requirements":[199],"low":[202],"operation":[203],"count":[204],"per":[205],"step":[206],"which":[207],"highly":[209],"efficient.":[210],"simultaneous":[212],"computation":[213],"improves":[220],"efficiency":[222],"stability":[225],"algorithm.":[228],"implementations":[231],"extensive":[233],"numerical":[234],"experiments":[235],"Circular":[238],"Restricted":[239],"Three":[240],"Body":[241],"Problem.":[242]},"counts_by_year":[],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2026-01-15T00:00:00"}
