{"id":"https://openalex.org/W2069023096","doi":"https://doi.org/10.1142/s0218127407019056","title":"GENERATION OF SYMMETRIC PERIODIC ORBITS BY A HETEROCLINIC LOOP FORMED BY TWO SINGULAR POINTS AND THEIR INVARIANT MANIFOLDS OF DIMENSIONS 1 AND 2 IN \u211d<sup>3</sup>","display_name":"GENERATION OF SYMMETRIC PERIODIC ORBITS BY A HETEROCLINIC LOOP FORMED BY TWO SINGULAR POINTS AND THEIR INVARIANT MANIFOLDS OF DIMENSIONS 1 AND 2 IN \u211d<sup>3</sup>","publication_year":2007,"publication_date":"2007-09-01","ids":{"openalex":"https://openalex.org/W2069023096","doi":"https://doi.org/10.1142/s0218127407019056","mag":"2069023096"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407019056","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019056","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://repositori.uvic-ucc.cat/bitstream/10854/2209/1/artconlli_a2007_corbera_montse_generation_symmetric_periodic.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020795093","display_name":"Montserrat Corbera","orcid":"https://orcid.org/0000-0002-0367-9667"},"institutions":[{"id":"https://openalex.org/I115304662","display_name":"Universitat de Vic - Universitat Central de Catalunya","ror":"https://ror.org/006zjws59","country_code":"ES","type":"education","lineage":["https://openalex.org/I115304662"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"MONTSERRAT CORBERA","raw_affiliation_strings":["Departament de Tecnologies Digitals i de la Informaci\u00f3, Universitat de Vic, 08500 Vic, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Tecnologies Digitals i de la Informaci\u00f3, Universitat de Vic, 08500 Vic, Barcelona, Spain","institution_ids":["https://openalex.org/I115304662"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046015548","display_name":"Jaume Llibre","orcid":"https://orcid.org/0000-0002-9511-5999"},"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"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"JAUME LLIBRE","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020795093"],"corresponding_institution_ids":["https://openalex.org/I115304662"],"apc_list":null,"apc_paid":null,"fwci":0.4543,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62904163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"09","first_page":"3295","last_page":"3302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":1.0,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9488000273704529,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6628625392913818},{"id":"https://openalex.org/keywords/heteroclinic-cycle","display_name":"Heteroclinic cycle","score":0.6109663248062134},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.596392035484314},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.5960522890090942},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5058164596557617},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.4986591339111328},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4966920018196106},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.48005494475364685},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4766553044319153},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.46408411860466003},{"id":"https://openalex.org/keywords/compactification","display_name":"Compactification (mathematics)","score":0.4234775900840759},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41743358969688416},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.2089238166809082},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2008979618549347},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.19687232375144958},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13710540533065796},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.10565739870071411}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6628625392913818},{"id":"https://openalex.org/C142115181","wikidata":"https://www.wikidata.org/wiki/Q16948232","display_name":"Heteroclinic cycle","level":5,"score":0.6109663248062134},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.596392035484314},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.5960522890090942},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5058164596557617},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.4986591339111328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4966920018196106},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.48005494475364685},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4766553044319153},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.46408411860466003},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.4234775900840759},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41743358969688416},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.2089238166809082},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2008979618549347},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.19687232375144958},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13710540533065796},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.10565739870071411},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127407019056","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019056","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:dspace.uvic.cat:10854/2209","is_oa":true,"landing_page_url":"http://hdl.handle.net/10854/2209","pdf_url":"https://repositori.uvic-ucc.cat/bitstream/10854/2209/1/artconlli_a2007_corbera_montse_generation_symmetric_periodic.pdf","source":{"id":"https://openalex.org/S4306401465","display_name":"Repositori Institucional De La Uvic (Universitat De Vic Universitat Central De Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115304662","host_organization_name":"Universitat de Vic - Universitat Central de Catalunya","host_organization_lineage":["https://openalex.org/I115304662"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dspace.uvic.cat:10854/2209","is_oa":true,"landing_page_url":"http://hdl.handle.net/10854/2209","pdf_url":"https://repositori.uvic-ucc.cat/bitstream/10854/2209/1/artconlli_a2007_corbera_montse_generation_symmetric_periodic.pdf","source":{"id":"https://openalex.org/S4306401465","display_name":"Repositori Institucional De La Uvic (Universitat De Vic Universitat Central De Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115304662","host_organization_name":"Universitat de Vic - Universitat Central de Catalunya","host_organization_lineage":["https://openalex.org/I115304662"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069023096.pdf","grobid_xml":"https://content.openalex.org/works/W2069023096.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1971650444","https://openalex.org/W1973434253","https://openalex.org/W2034747258","https://openalex.org/W2042498362","https://openalex.org/W2092680287","https://openalex.org/W2792049198","https://openalex.org/W4210605524"],"related_works":["https://openalex.org/W2040151997","https://openalex.org/W1497977526","https://openalex.org/W2159719320","https://openalex.org/W2008693397","https://openalex.org/W2151523878","https://openalex.org/W2066526839","https://openalex.org/W2373813151","https://openalex.org/W3115753373","https://openalex.org/W2788862548","https://openalex.org/W2595758916"],"abstract_inverted_index":{"In":[0,107],"this":[1],"paper":[2],"we":[3],"will":[4],"find":[5],"continuous":[6],"periodic":[7,139],"orbits":[8,140],"passing":[9],"near":[10],"infinity":[11,58,115],"for":[12,133],"a":[13,32,37,43,145],"class":[14],"of":[15,71,102,137,144],"polynomial":[16,25],"vector":[17,26],"fields":[18,27],"in":[19,89,116],"\u211d":[20,90],"3":[21,91],".":[22,129],"We":[23],"consider":[24],"that":[28,41],"are":[29],"invariant":[30,61,69,100],"under":[31],"symmetry":[33,156],"with":[34,154,157],"respect":[35,158],"to":[36,82,95,159],"plane":[38],"\u03a3":[39],"and":[40,54,59,64,92,126],"possess":[42],"\"generalized":[44],"heteroclinic":[45,151],"loop\"":[46],"formed":[47,74],"by":[48,75],"two":[49],"singular":[50,122],"points":[51,123],"e":[52,55,80,83,124,127],"+":[53,84,125],"-":[56,81,128],"at":[57,105,114],"their":[60],"manifolds":[62],"\u0393":[63,66,86],"\u039b.":[65],"is":[67,87,93,98,110,141],"an":[68,76,99],"manifold":[70,101],"dimension":[72,103],"1":[73],"orbit":[77],"going":[78],"from":[79],",":[85],"contained":[88],"transversal":[94],"\u03a3.":[96,160],"\u039b":[97,109],"2":[104],"infinity.":[106],"fact,":[108],"the":[111,117,121,135,142,149,155],"two-dimensional":[112],"sphere":[113],"Poincar\u00e9":[118,146],"compactification":[119],"minus":[120],"The":[130],"main":[131],"tool":[132],"proving":[134],"existence":[136],"such":[138],"construction":[143],"map":[147],"along":[148],"generalized":[150],"loop":[152],"together":[153]},"counts_by_year":[],"updated_date":"2026-03-17T17:19:04.345684","created_date":"2025-10-10T00:00:00"}