{"id":"https://openalex.org/W4362466422","doi":"https://doi.org/10.3390/axioms12040342","title":"Limit Cycles of Polynomially Integrable Piecewise Differential Systems","display_name":"Limit Cycles of Polynomially Integrable Piecewise Differential Systems","publication_year":2023,"publication_date":"2023-03-31","ids":{"openalex":"https://openalex.org/W4362466422","doi":"https://doi.org/10.3390/axioms12040342"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12040342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12040342","pdf_url":"https://www.mdpi.com/2075-1680/12/4/342/pdf?version=1680253144","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/4/342/pdf?version=1680253144","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110967504","display_name":"Bel\u00e9n Garc\u00eda","orcid":null},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Bel\u00e9n Garc\u00eda","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Oviedo, Avda Calvo Sotelo s/n, 33007 Oviedo, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Oviedo, Avda Calvo Sotelo s/n, 33007 Oviedo, Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"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":true,"raw_author_name":"Jaume Llibre","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Bellaterra, 08193 Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9511-5999","affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, Bellaterra, 08193 Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042954914","display_name":"Jes\u00fas S. P\u00e9rez del R\u0131\u0301o","orcid":"https://orcid.org/0000-0003-0003-0157"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jes\u00fas S. P\u00e9rez del R\u00edo","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Oviedo, Avda Calvo Sotelo s/n, 33007 Oviedo, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Oviedo, Avda Calvo Sotelo s/n, 33007 Oviedo, Spain","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000784084","display_name":"Set P\u00e9rez-Gonz\u00e1lez","orcid":"https://orcid.org/0000-0002-1522-7086"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Set P\u00e9rez-Gonz\u00e1lez","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Oviedo, Avda Calvo Sotelo s/n, 33007 Oviedo, Spain"],"raw_orcid":"https://orcid.org/0000-0002-1522-7086","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Oviedo, Avda Calvo Sotelo s/n, 33007 Oviedo, Spain","institution_ids":["https://openalex.org/I165339363"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046015548"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.627,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80737884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"12","issue":"4","first_page":"342","last_page":"342"},"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":0.7855161428451538},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7605679631233215},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.7598092555999756},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.7315386533737183},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6562082767486572},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5408118367195129},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5387791991233826},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5212422013282776},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48923206329345703},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4889275133609772},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4515777826309204},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35858356952667236},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09478756785392761}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7855161428451538},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7605679631233215},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.7598092555999756},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.7315386533737183},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6562082767486572},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5408118367195129},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5387791991233826},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5212422013282776},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48923206329345703},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4889275133609772},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4515777826309204},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35858356952667236},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09478756785392761},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms12040342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12040342","pdf_url":"https://www.mdpi.com/2075-1680/12/4/342/pdf?version=1680253144","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:ddd.uab.cat:275853","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/275853","pdf_url":"https://ddd.uab.cat/pub/poncom/2023/f3f42aad3da2/axioms_12_00342.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"},{"id":"pmh:oai:doaj.org/article:6339bad697a445d1be13f563fbd50fd0","is_oa":true,"landing_page_url":"https://doaj.org/article/6339bad697a445d1be13f563fbd50fd0","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 4, p 342 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/4/342/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12040342","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Axioms; Volume 12; Issue 4; Pages: 342","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12040342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12040342","pdf_url":"https://www.mdpi.com/2075-1680/12/4/342/pdf?version=1680253144","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1423109669","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"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/G2436355136","display_name":null,"funder_award_id":"MSCA-RISE-2017","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G2548492180","display_name":null,"funder_award_id":"2017-777911","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G3243401500","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"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/G4161175669","display_name":null,"funder_award_id":"PID2019-104658GB-I00","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G4886544318","display_name":null,"funder_award_id":"MCI-21-PID2020-113052GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5175525644","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G526235227","display_name":null,"funder_award_id":"777911","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G6059518138","display_name":null,"funder_award_id":"MSCA-RISE-2017-777911","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G615366877","display_name":null,"funder_award_id":"PID2020-113052GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"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"},{"id":"https://openalex.org/G6389653320","display_name":null,"funder_award_id":"grant PID2019-104658GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6764922704","display_name":null,"funder_award_id":"2022-SGR 00113","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G683931746","display_name":null,"funder_award_id":"H2020","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7425137858","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G7944295140","display_name":null,"funder_award_id":"H2020","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G8684520763","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320321505","display_name":"Generalitat de Catalunya","ror":"https://ror.org/01bg62x04"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334830","display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","ror":"https://ror.org/01n4pqe45"},{"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":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4362466422.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W2017155383","https://openalex.org/W2033982406","https://openalex.org/W2042192623","https://openalex.org/W2054652000","https://openalex.org/W2624476619","https://openalex.org/W2796609112","https://openalex.org/W2951830236","https://openalex.org/W4230378422","https://openalex.org/W4286973255","https://openalex.org/W4293078920","https://openalex.org/W4309683868","https://openalex.org/W6739204642"],"related_works":["https://openalex.org/W1011288031","https://openalex.org/W1965043874","https://openalex.org/W1577606234","https://openalex.org/W1916844891","https://openalex.org/W25683132","https://openalex.org/W25827740","https://openalex.org/W88265998","https://openalex.org/W4394656111","https://openalex.org/W1992045028","https://openalex.org/W1634204107"],"abstract_inverted_index":{"In":[0],"this":[1,41],"paper,":[2],"we":[3],"study":[4,54],"how":[5],"many":[6],"algebraic":[7],"limit":[8,51],"cycles":[9],"have":[10,46],"the":[11,36],"discontinuous":[12],"piecewise":[13,43],"linear":[14,56],"differential":[15,44,57],"systems":[16,37,45,58],"separated":[17],"by":[18],"a":[19],"straight":[20],"line,":[21],"with":[22,59],"polynomial":[23,60],"first":[24,61],"integrals":[25],"on":[26],"both":[27],"sides.":[28],"We":[29],"assume":[30],"that":[31],"at":[32],"least":[33],"one":[34,50],"of":[35],"is":[38],"Hamiltonian.":[39],"Under":[40],"assumption,":[42],"no":[47],"more":[48],"than":[49],"cycle.":[52],"This":[53],"characterizes":[55],"integrals.":[62]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-01-21T23:30:37.877113","created_date":"2025-10-10T00:00:00"}
