{"id":"https://openalex.org/W4207025883","doi":"https://doi.org/10.1142/s0218127422500031","title":"Limit Cycles of Continuous Piecewise Differential Systems Formed by Linear and Quadratic Isochronous Centers I","display_name":"Limit Cycles of Continuous Piecewise Differential Systems Formed by Linear and Quadratic Isochronous Centers I","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4207025883","doi":"https://doi.org/10.1142/s0218127422500031"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127422500031","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422500031","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/257103","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039354327","display_name":"Bilal Ghermoul","orcid":"https://orcid.org/0000-0003-0617-9665"},"institutions":[{"id":"https://openalex.org/I4210135256","display_name":"University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj","ror":"https://ror.org/03e75b898","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210135256"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Bilal Ghermoul","raw_affiliation_strings":["Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria"],"raw_orcid":"https://orcid.org/0000-0003-0617-9665","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria","institution_ids":["https://openalex.org/I4210135256"]}]},{"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"],"raw_orcid":null,"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/A5008023400","display_name":"Tayeb Salhi","orcid":"https://orcid.org/0000-0003-1220-592X"},"institutions":[{"id":"https://openalex.org/I4210135256","display_name":"University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj","ror":"https://ror.org/03e75b898","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210135256"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Tayeb Salhi","raw_affiliation_strings":["Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34265, El\u2013Anasser, Algeria","institution_ids":["https://openalex.org/I4210135256"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039354327"],"corresponding_institution_ids":["https://openalex.org/I4210135256"],"apc_list":null,"apc_paid":null,"fwci":0.4019,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.53615855,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"32","issue":"01","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/piecewise","display_name":"Piecewise","score":0.737139105796814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6858057975769043},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.681586503982544},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6095425486564636},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.5380269289016724},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5137418508529663},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.46696382761001587},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45773956179618835},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.44975417852401733},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.42723965644836426},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34972596168518066},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17419302463531494},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1416252851486206}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.737139105796814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6858057975769043},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.681586503982544},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6095425486564636},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5380269289016724},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5137418508529663},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.46696382761001587},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45773956179618835},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.44975417852401733},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.42723965644836426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34972596168518066},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17419302463531494},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1416252851486206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"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/s0218127422500031","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127422500031","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:257103","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/257103","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"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:257103","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/257103","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W965103837","https://openalex.org/W1992299830","https://openalex.org/W2049815318","https://openalex.org/W2182274314","https://openalex.org/W2765944944"],"related_works":["https://openalex.org/W4206327962","https://openalex.org/W2361025465","https://openalex.org/W2725010352","https://openalex.org/W2010009304","https://openalex.org/W2385263368","https://openalex.org/W2765944944","https://openalex.org/W4226164715","https://openalex.org/W3096660584","https://openalex.org/W2243882821","https://openalex.org/W2048650277"],"abstract_inverted_index":{"First,":[0],"we":[1,58,148],"study":[2,59],"the":[3,11,60,68,76,87,120,151,154],"planar":[4,69],"continuous":[5,70,116,144],"piecewise":[6,40,71,117,145],"differential":[7,41,72,118,146],"systems":[8,42,73,119,147],"separated":[9,74],"by":[10,18,75],"straight":[12,77],"line":[13,78],"[Formula:":[14,24,33,79,84,92,95,104],"see":[15,25,34,80,85,93,96,105],"text]":[16,26,81,86,97,106],"formed":[17],"a":[19],"linear":[20],"isochronous":[21,29,90,110],"center":[22,31,91],"in":[23,32,83,103],"and":[27,48,64,102,129],"an":[28,99,107],"quadratic":[30,89,109],"text].":[35],"We":[36],"prove":[37],"that":[38],"these":[39,113,141],"cannot":[43],"have":[44,53,149],"crossing":[45,54,61,124,135],"periodic":[46,62],"orbits,":[47],"consequently":[49],"they":[50],"do":[51],"not":[52],"limit":[55,65,125,136],"cycles.":[56,137],"Second,":[57],"orbits":[63],"cycles":[66,126],"of":[67,115,123,143,153],"having":[82,133],"general":[88],"text],":[94],"after":[98],"affine":[100],"transformation,":[101],"arbitrary":[108],"center.":[111],"For":[112],"kind":[114],"maximum":[121],"number":[122],"is":[127],"one,":[128],"there":[130],"are":[131],"examples":[132],"one":[134],"In":[138],"short":[139],"for":[140],"families":[142],"solved":[150],"extension":[152],"16th":[155],"Hilbert":[156],"problem.":[157]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
