{"id":"https://openalex.org/W4390823277","doi":"https://doi.org/10.1137/23m1561257","title":"Flow Map Parameterization Methods for Invariant Tori in Quasi-Periodic Hamiltonian Systems","display_name":"Flow Map Parameterization Methods for Invariant Tori in Quasi-Periodic Hamiltonian Systems","publication_year":2024,"publication_date":"2024-01-12","ids":{"openalex":"https://openalex.org/W4390823277","doi":"https://doi.org/10.1137/23m1561257"},"language":"en","primary_location":{"id":"doi:10.1137/23m1561257","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1561257","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ddd.uab.cat/pub/artpub/2024/299745/FerHarMon2024a-Preprint.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006911008","display_name":"\u00c1lvaro Fern\u00e1ndez-Mora","orcid":"https://orcid.org/0000-0002-3863-0003"},"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/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":["CERES-IEEC, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain","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":"CERES-IEEC, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]},{"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/A5052725846","display_name":"\u00c0lex Haro","orcid":"https://orcid.org/0000-0003-0377-8099"},"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":"Alex Haro","raw_affiliation_strings":["Centre de Recerca Matem\u00e0tica, Edifici C, Campus Bellaterra, 08193 Bellaterra, Barcelona, 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, Barcelona, 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":"last","author":{"id":"https://openalex.org/A5013346824","display_name":"Josep\u2013Maria Mondelo","orcid":"https://orcid.org/0000-0002-7135-0599"},"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":"J. M. Mondelo","raw_affiliation_strings":["CERES-IEEC, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain","Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Av.\u00a0de l\u2019Eix Central, Edifici C, 08193 Bellaterra, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERES-IEEC, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]},{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Av.\u00a0de l\u2019Eix Central, Edifici C, 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942","https://openalex.org/I4210122226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006911008"],"corresponding_institution_ids":["https://openalex.org/I123044942","https://openalex.org/I71999127"],"apc_list":null,"apc_paid":null,"fwci":1.859,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.83995107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"23","issue":"1","first_page":"127","last_page":"166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9998000264167786,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7548055648803711},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7326566576957703},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6751771569252014},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.6002574563026428},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5340873599052429},{"id":"https://openalex.org/keywords/quasiperiodic-function","display_name":"Quasiperiodic function","score":0.5061361193656921},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.45189666748046875},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4268343448638916},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.41644710302352905},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3764435946941376},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3693721890449524},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16085243225097656},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07758572697639465}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7548055648803711},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7326566576957703},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6751771569252014},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.6002574563026428},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5340873599052429},{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.5061361193656921},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.45189666748046875},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4268343448638916},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.41644710302352905},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3764435946941376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3693721890449524},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16085243225097656},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07758572697639465},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1561257","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1561257","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:ddd.uab.cat:299745","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/299745","pdf_url":"https://ddd.uab.cat/pub/artpub/2024/299745/FerHarMon2024a-Preprint.pdf","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:299745","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/299745","pdf_url":"https://ddd.uab.cat/pub/artpub/2024/299745/FerHarMon2024a-Preprint.pdf","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3256183407","display_name":null,"funder_award_id":"SGR 00113","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"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/G546218868","display_name":null,"funder_award_id":"2021 SGR 00113","funder_id":"https://openalex.org/F4320321506","funder_display_name":"Consell Catal\u00e0 de Recerca i Innovaci\u00f3"},{"id":"https://openalex.org/G5489373891","display_name":null,"funder_award_id":"2021 SGR 00113","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G5712420156","display_name":"Stability and Transitions in Physical Processes","funder_award_id":"734557","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"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/G6325762137","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"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/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321505","display_name":"Generalitat de Catalunya","ror":"https://ror.org/01bg62x04"},{"id":"https://openalex.org/F4320321506","display_name":"Consell Catal\u00e0 de Recerca i Innovaci\u00f3","ror":null},{"id":"https://openalex.org/F4320323428","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57"},{"id":"https://openalex.org/F4320326826","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320337907","display_name":"Integrated Electronics Engineering Center, Binghamton University","ror":null},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390823277.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W44921523","https://openalex.org/W78381459","https://openalex.org/W1533633043","https://openalex.org/W1538690802","https://openalex.org/W1679852829","https://openalex.org/W1989018928","https://openalex.org/W1993430945","https://openalex.org/W1996087276","https://openalex.org/W2000280157","https://openalex.org/W2001742524","https://openalex.org/W2013946715","https://openalex.org/W2026806341","https://openalex.org/W2036319645","https://openalex.org/W2067503369","https://openalex.org/W2080409870","https://openalex.org/W2087723889","https://openalex.org/W2144712788","https://openalex.org/W2160163816","https://openalex.org/W2166776051","https://openalex.org/W2186590998","https://openalex.org/W2326458513","https://openalex.org/W2335681000","https://openalex.org/W2389184278","https://openalex.org/W2594779596","https://openalex.org/W2613178133","https://openalex.org/W2613939086","https://openalex.org/W2963039554","https://openalex.org/W2963881724","https://openalex.org/W2996339364","https://openalex.org/W3026351915","https://openalex.org/W3124331571","https://openalex.org/W3166162485","https://openalex.org/W3170594448","https://openalex.org/W3172724430","https://openalex.org/W4245651583","https://openalex.org/W4296477255"],"related_works":["https://openalex.org/W2024715358","https://openalex.org/W4321392735","https://openalex.org/W2783675181","https://openalex.org/W2483840363","https://openalex.org/W25827740","https://openalex.org/W4387063326","https://openalex.org/W2010444946","https://openalex.org/W2962845032","https://openalex.org/W2921481273","https://openalex.org/W2027000851"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,13,44,76,83,85],"this":[3,38],"paper":[4],"is":[5],"to":[6,10,33,65,73],"present":[7],"a":[8,68],"method":[9],"compute":[11,100],"parameterizations":[12],"partially":[14],"hyperbolic":[15],"invariant":[16,20,103,107],"tori":[17,47,104],"and":[18,48,51,57,71,99,105],"their":[19,58,106],"bundles":[21,108],"in":[22,67,92],"nonautonomous":[23],"quasi-periodic":[24,35],"Hamiltonian":[25],"systems.":[26],"We":[27,88],"generalize":[28],"flow":[29],"map":[30],"parameterization":[31],"methods":[32],"the":[34,42,74,81,93,110],"setting.":[36],"To":[37],"end,":[39],"we":[40],"introduce":[41],"notion":[43],"fiberwise":[45,54],"isotropic":[46],"sketch":[49],"definitions":[50],"results":[52],"on":[53],"symplectic":[55],"deformations":[56],"moment":[59],"maps.":[60],"These":[61],"constructs":[62],"are":[63],"vital":[64],"work":[66],"suitable":[69],"setting":[70],"lead":[72],"proofs":[75],"''magic":[77],"cancellations\"":[78],"that":[79],"guarantee":[80],"existence":[82],"solutions":[84],"cohomological":[86],"equations.":[87],"apply":[89],"our":[90],"algorithms":[91],"elliptic":[94],"restricted":[95],"three":[96],"body":[97],"problem":[98],"nonresonant":[101],"3-dimensional":[102],"around":[109],"L1":[111],"point.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}