{"id":"https://openalex.org/W2046567429","doi":"https://doi.org/10.1142/s0218127411029501","title":"GLOBAL CLASSIFICATION OF A CLASS OF CUBIC VECTOR FIELDS WHOSE CANONICAL REGIONS ARE PERIOD ANNULI","display_name":"GLOBAL CLASSIFICATION OF A CLASS OF CUBIC VECTOR FIELDS WHOSE CANONICAL REGIONS ARE PERIOD ANNULI","publication_year":2011,"publication_date":"2011-04-05","ids":{"openalex":"https://openalex.org/W2046567429","doi":"https://doi.org/10.1142/s0218127411029501","mag":"2046567429"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127411029501","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411029501","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://ddd.uab.cat/record/150445","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059573612","display_name":"Magdalena Caubergh","orcid":"https://orcid.org/0000-0001-7358-2839"},"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"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. CAUBERGH","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I4210122226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046015548","display_name":"Jaume Llibre","orcid":"https://orcid.org/0000-0002-9511-5999"},"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"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. LLIBRE","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I4210122226"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085767356","display_name":"Joan Torregrosa","orcid":"https://orcid.org/0000-0002-2753-1827"},"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"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. TORREGROSA","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Edifici C. 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I4210122226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210122226"],"apc_list":null,"apc_paid":null,"fwci":2.2206,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.87207553,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"07","first_page":"1831","last_page":"1867"},"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9660999774932861,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9332000017166138,"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/phase-portrait","display_name":"Phase portrait","score":0.7911368608474731},{"id":"https://openalex.org/keywords/quintic-function","display_name":"Quintic function","score":0.7711814641952515},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6437208652496338},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6231773495674133},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5472015738487244},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5166659355163574},{"id":"https://openalex.org/keywords/diffeomorphism","display_name":"Diffeomorphism","score":0.44394034147262573},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41130805015563965},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3809521496295929},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3656216859817505},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3531787395477295},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3186008930206299},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2872188687324524},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19729959964752197},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14857304096221924},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1105697751045227}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.7911368608474731},{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.7711814641952515},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6437208652496338},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6231773495674133},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5472015738487244},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5166659355163574},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.44394034147262573},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41130805015563965},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3809521496295929},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3656216859817505},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3531787395477295},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3186008930206299},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2872188687324524},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19729959964752197},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14857304096221924},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1105697751045227},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127411029501","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411029501","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:ddd.uab.cat:150445","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/150445","pdf_url":null,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:dnet:uabarcelona_::f63c86b0a108c8a1f4a16b7748ec7a74","is_oa":false,"landing_page_url":"http://ddd.uab.cat/record/150445","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:150445","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/150445","pdf_url":null,"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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6000000238418579}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W625401248","https://openalex.org/W1607000426","https://openalex.org/W1969152209","https://openalex.org/W1971136638","https://openalex.org/W1972241390","https://openalex.org/W1982717554","https://openalex.org/W1990453709","https://openalex.org/W1995028922","https://openalex.org/W2000286527","https://openalex.org/W2028532048","https://openalex.org/W2029058241","https://openalex.org/W2030479805","https://openalex.org/W2035001720","https://openalex.org/W2042966107","https://openalex.org/W2043302122","https://openalex.org/W2054175266","https://openalex.org/W2074354330","https://openalex.org/W2076472288","https://openalex.org/W2089729261","https://openalex.org/W2089956833","https://openalex.org/W2094231262","https://openalex.org/W2163453170","https://openalex.org/W2331106233","https://openalex.org/W2360966310","https://openalex.org/W2482135575"],"related_works":["https://openalex.org/W2339458745","https://openalex.org/W4254786939","https://openalex.org/W4238758668","https://openalex.org/W4302555561","https://openalex.org/W4310230578","https://openalex.org/W4389939874","https://openalex.org/W3110175929","https://openalex.org/W2310202934","https://openalex.org/W2907443228","https://openalex.org/W2097333826"],"abstract_inverted_index":{"We":[0],"study":[1,154],"cubic":[2,55,99],"vector":[3],"fields":[4],"with":[5,176],"inverse":[6],"radial":[7],"symmetry,":[8],"i.e.":[9],"of":[10,71,92,97,148,158,162,180],"the":[11,46,72,89,93,98,127,134,155],"form":[12],"\u1e8b":[13],"=":[14,28,106],"\u03b4x":[15],"-":[16,24],"y":[17],"+":[18,21,30,32,35,38],"ax2+":[19],"bxy":[20],"cy2+":[22],"\u03c3(dx":[23],"y)(x2+":[25],"y2),":[26,41],"\u1e8f":[27],"x":[29],"\u03b4y":[31],"ex2+":[33],"fxy":[34],"gy2+":[36],"\u03c3(x":[37],"dy)":[39],"(x2+":[40],"having":[42],"a":[43,81,159,172,177],"center":[44],"at":[45,49],"origin":[47],"and":[48,78,111,186],"infinity;":[50],"we":[51,67,79,138,153,167],"shortly":[52],"call":[53],"them":[54],"irs-systems.":[56,165],"These":[57],"systems":[58,77],"are":[59,117],"known":[60],"to":[61,109,141,145,170],"be":[62],"Hamiltonian":[63,100,128,164],"or":[64],"reversible.":[65],"Here":[66],"provide":[68],"an":[69],"improvement":[70],"algorithm":[73],"that":[74],"characterizes":[75],"these":[76],"give":[80],"new":[82],"normal":[83],"form.":[84],"Our":[85],"main":[86],"result":[87],"is":[88],"systematic":[90],"classification":[91],"global":[94,123],"phase":[95,124],"portraits":[96,125],"irs-systems":[101,132,147],"respecting":[102,182],"time":[103],"(i.e.":[104],"\u03c3":[105],"1)":[107],"up":[108],"topological":[110,184],"diffeomorphic":[112],"equivalence.":[113],"In":[114,151],"particular,":[115,152],"there":[116],"22":[118],"(resp.":[119,129],"14)":[120],"topologically":[121],"different":[122],"for":[126],"reversible":[130,174],"Hamiltonian)":[131],"on":[133],"Poincar\u00e9":[135],"disc.":[136],"Finally":[137],"illustrate":[139],"how":[140,169],"generalize":[142],"our":[143],"results":[144],"polynomial":[146],"arbitrary":[149],"degree.":[150],"bifurcation":[156],"diagram":[157],"1-parameter":[160],"subfamily":[161],"quintic":[163],"Moreover,":[166],"indicate":[168],"construct":[171],"concrete":[173],"irs-system":[175],"given":[178],"configuration":[179],"singularities":[181],"their":[183],"type":[185],"separatrix":[187],"connections.":[188]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-10-10T00:00:00"}
