{"id":"https://openalex.org/W2162071908","doi":"https://doi.org/10.1137/040614517","title":"Approximating the Invariant Sets of a Finite Straight Segment near Its Collinear Equilibria","display_name":"Approximating the Invariant Sets of a Finite Straight Segment near Its Collinear Equilibria","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2162071908","doi":"https://doi.org/10.1137/040614517","mag":"2162071908"},"language":"en","primary_location":{"id":"doi:10.1137/040614517","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040614517","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075274359","display_name":"Jes\u00fas F. Palaci\u00e1n","orcid":"https://orcid.org/0000-0002-0974-6656"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jes\u00fas F. Palaci\u00e1n","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060236004","display_name":"Patricia Yanguas","orcid":"https://orcid.org/0000-0001-9767-5554"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patricia Yanguas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084815328","display_name":"Susana Guti\u00e9rrez-Romero","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Susana Guti\u00e9rrez-Romero","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.20652025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"5","issue":"1","first_page":"12","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9995999932289124,"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":0.9995999932289124,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9746999740600586,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/hamiltonian-system","display_name":"Hamiltonian system","score":0.6875720024108887},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6256811618804932},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5701156258583069},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.566379964351654},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.565600574016571},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.524674117565155},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.5142983794212341},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.476071298122406},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.448543518781662},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.4337001442909241},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":0.43344366550445557},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.4225023090839386},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4054570198059082},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32400810718536377},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.2581654191017151},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2029760181903839},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1296091377735138},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11340507864952087},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.09972575306892395},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07917743921279907},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.07149958610534668}],"concepts":[{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6875720024108887},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6256811618804932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5701156258583069},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.566379964351654},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.565600574016571},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.524674117565155},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.5142983794212341},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.476071298122406},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.448543518781662},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.4337001442909241},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.43344366550445557},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.4225023090839386},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4054570198059082},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32400810718536377},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.2581654191017151},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2029760181903839},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1296091377735138},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11340507864952087},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.09972575306892395},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07917743921279907},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07149958610534668},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040614517","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040614517","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7799999713897705}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W9659652","https://openalex.org/W38412343","https://openalex.org/W74804614","https://openalex.org/W133774097","https://openalex.org/W201997521","https://openalex.org/W1579475312","https://openalex.org/W1964312819","https://openalex.org/W1967579835","https://openalex.org/W1968611432","https://openalex.org/W2005837982","https://openalex.org/W2009334861","https://openalex.org/W2012068782","https://openalex.org/W2019229714","https://openalex.org/W2042301878","https://openalex.org/W2071290058","https://openalex.org/W2087723889","https://openalex.org/W2109599407","https://openalex.org/W2121511041","https://openalex.org/W2124529968","https://openalex.org/W2134402432","https://openalex.org/W2184987017","https://openalex.org/W4237872277"],"related_works":["https://openalex.org/W2243875171","https://openalex.org/W3021060928","https://openalex.org/W2087723889","https://openalex.org/W2077286646","https://openalex.org/W1983459863","https://openalex.org/W2129195111","https://openalex.org/W1536954903","https://openalex.org/W2041496883","https://openalex.org/W194084237","https://openalex.org/W4236903077"],"abstract_inverted_index":{"This":[0],"paper":[1],"reviews":[2],"a":[3,74,78],"method":[4,31],"for":[5],"computing":[6],"explicitly":[7],"the":[8,16,35,46,55,60,66,71,93,98,102,108,112,119,125,138,140,143,147,151,157,163,170,183,190,193,197,213],"asymptotic":[9],"expressions":[10],"of":[11,18,25,28,37,48,57,59,73,85,101,124,131,146,154,156,192,212],"some":[12,209],"invariant":[13,166,184],"manifolds":[14,145],"in":[15,189],"vicinity":[17],"equilibrium":[19,62,194],"points":[20,63],"corresponding":[21,64,96],"to":[22,44,54,65,97,111,122,136,207],"Hamiltonian":[23,67,109,120,200],"systems":[24],"m":[26],"degrees":[27],"freedom.":[29],"The":[30],"is":[32,43],"based":[33],"on":[34],"use":[36,84],"generalized":[38],"normal":[39,198],"forms.":[40],"Our":[41],"goal":[42],"show":[45],"power":[47],"this":[49],"technique":[50],"by":[51,70,202],"applying":[52],"it":[53],"study":[56],"one":[58,123],"colinear":[61,103],"system":[68,149],"defined":[69],"motion":[72],"particle":[75],"orbiting":[76],"around":[77],"finite":[79],"straight":[80],"segment.":[81],"We":[82,160],"make":[83],"three":[86],"different":[87],"Lie":[88],"transformations:":[89],"(i)":[90],"we":[91,106,117,133,181,204],"calculate":[92],"Hamilton":[94],"function":[95],"center":[99],"manifold":[100,167],"equilibrium;":[104],"(ii)":[105],"determine":[107,208],"related":[110,121],"stable-unstable":[113],"direction;":[114],"and":[115,142,176,186],"(iii)":[116,203],"obtain":[118],"two":[126,158],"stable-stable":[127],"directions.":[128],"By":[129],"means":[130],"(i),":[132],"are":[134,205],"able":[135,206],"parameterize":[137],"center,":[139],"stable,":[141],"unstable":[144,177],"original":[148],"using":[150],"direct":[152],"changes":[153],"coordinates":[155],"transformations.":[159],"also":[161],"compute":[162,182],"normally":[164],"hyperbolic":[165],"associated":[168],"with":[169,173],"equilibrium,":[171],"together":[172],"its":[174],"stable":[175],"manifolds.":[178],"Using":[179],"(ii),":[180],"2-tori":[185],"quasi-periodic":[187],"orbits":[188,211],"neighborhood":[191],"chosen.":[195],"Through":[196],"form":[199],"obtained":[201],"periodic":[210],"initial":[214],"Hamiltonian.":[215]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}