{"id":"https://openalex.org/W4304889874","doi":"https://doi.org/10.1142/s021812742250184x","title":"Limit Cycles of Planar Discontinuous Piecewise Linear Hamiltonian Systems Without Equilibria Separated by Nonregular Curves","display_name":"Limit Cycles of Planar Discontinuous Piecewise Linear Hamiltonian Systems Without Equilibria Separated by Nonregular Curves","publication_year":2022,"publication_date":"2022-09-30","ids":{"openalex":"https://openalex.org/W4304889874","doi":"https://doi.org/10.1142/s021812742250184x"},"language":"en","primary_location":{"id":"doi:10.1142/s021812742250184x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742250184x","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/268646","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042527112","display_name":"Johana Jimenez","orcid":"https://orcid.org/0000-0002-3378-4679"},"institutions":[{"id":"https://openalex.org/I2802951768","display_name":"Universidade Federal do Oeste da Bahia","ror":"https://ror.org/03raeyn57","country_code":"BR","type":"education","lineage":["https://openalex.org/I2802951768"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Johana Jimenez","raw_affiliation_strings":["Universidade Federal do Oeste da Bahia, 47600000 Bom Jesus da Lapa, Bahia, Brazil"],"affiliations":[{"raw_affiliation_string":"Universidade Federal do Oeste da Bahia, 47600000 Bom Jesus da Lapa, Bahia, Brazil","institution_ids":["https://openalex.org/I2802951768"]}]},{"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/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, Catalonia, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070562969","display_name":"Cl\u00e0ud\u00eca Valls","orcid":"https://orcid.org/0000-0001-8279-1229"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I203847022","display_name":"Instituto Polit\u00e9cnico de Lisboa","ror":"https://ror.org/04ea70f07","country_code":"PT","type":"education","lineage":["https://openalex.org/I203847022"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Claudia Valls","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1049\u2013001, Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais 1049\u2013001, Lisboa, Portugal","institution_ids":["https://openalex.org/I203847022","https://openalex.org/I141596103"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042527112"],"corresponding_institution_ids":["https://openalex.org/I2802951768"],"apc_list":null,"apc_paid":null,"fwci":0.7993,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70212465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"32","issue":"12","first_page":null,"last_page":null},"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":0.9998999834060669,"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":0.9998999834060669,"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/mathematics","display_name":"Mathematics","score":0.8273028135299683},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6820651888847351},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6684593558311462},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6554805040359497},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6469947099685669},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.6365349292755127},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6042885780334473},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5244809985160828},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4395413100719452},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.426422119140625},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41979917883872986},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3426089286804199},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17722561955451965},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08603101968765259},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07646343111991882},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06840026378631592}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8273028135299683},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6820651888847351},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6684593558311462},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6554805040359497},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6469947099685669},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.6365349292755127},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6042885780334473},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5244809985160828},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4395413100719452},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.426422119140625},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41979917883872986},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3426089286804199},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17722561955451965},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08603101968765259},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07646343111991882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06840026378631592},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s021812742250184x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742250184x","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:268646","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/268646","pdf_url":null,"source":{"id":"https://openalex.org/S4306400381","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"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:268646","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/268646","pdf_url":null,"source":{"id":"https://openalex.org/S4306400381","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":[],"awards":[{"id":"https://openalex.org/G2133003115","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G618704488","display_name":null,"funder_award_id":"PID2019-104658GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1552094772","https://openalex.org/W1558079603","https://openalex.org/W2002282594","https://openalex.org/W2037024940","https://openalex.org/W2042192623","https://openalex.org/W2050710621","https://openalex.org/W2053658423","https://openalex.org/W2092046534","https://openalex.org/W2135003992","https://openalex.org/W2923762604","https://openalex.org/W2964858335","https://openalex.org/W3020980268","https://openalex.org/W3088944815","https://openalex.org/W4230378422","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W4226164715","https://openalex.org/W3096660584","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W3208509670","https://openalex.org/W2109304297","https://openalex.org/W2100864966","https://openalex.org/W2058567245"],"abstract_inverted_index":{"The":[0],"problem":[1,25],"of":[2,10,14,30,40,61],"determining":[3],"the":[4,11,15,27,58,86],"existence,":[5],"maximum":[6,59,74],"number":[7,60],"and":[8,70],"positions":[9],"limit":[12,63],"cycles":[13,64],"planar":[16],"discontinuous":[17],"piecewise":[18,41],"linear":[19,42],"differential":[20,31],"systems":[21,44],"is":[22,75],"an":[23],"important":[24],"in":[26,47],"qualitative":[28],"theory":[29],"systems.":[32],"In":[33,77],"this":[34,73,78],"paper,":[35],"we":[36,80],"study":[37],"two":[38],"families":[39],"Hamiltonian":[43],"without":[45],"equilibria":[46],"[Formula:":[48],"see":[49],"text]":[50],"separated":[51],"by":[52],"a":[53],"nonregular":[54],"curve.":[55],"We":[56],"provide":[57],"crossing":[62],"that":[65],"each":[66,84],"family":[67,85],"can":[68],"have":[69],"show":[71],"when":[72],"reached.":[76],"way":[79],"are":[81],"solving":[82],"for":[83],"extended":[87],"16th":[88],"Hilbert":[89],"problem.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}