{"id":"https://openalex.org/W7220971349","doi":"https://doi.org/10.48550/arxiv.2610.08725","title":"Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles","display_name":"Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220971349","doi":"https://doi.org/10.48550/arxiv.2610.08725"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08725","pdf_url":"https://arxiv.org/pdf/2610.08725","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.08725","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157951630","display_name":"Carlos Vin\u00edcius das Neves Silva","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Silva, Carlos Vin\u00edcius das Neves","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5157916069","display_name":"Paulo Ricardo da Silva","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"da Silva, Paulo Ricardo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9990000128746033,"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":0.9990000128746033,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/limit-cycles","display_name":"limit cycles","score":0.8650000095367432},{"id":"https://openalex.org/keywords/bifurcation","display_name":"bifurcation","score":0.8629999756813049},{"id":"https://openalex.org/keywords/linear-center","display_name":"linear center","score":0.828000009059906},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"periodic orbits","score":0.871999979019165},{"id":"https://openalex.org/keywords/zones","display_name":"zones","score":0.36000001430511475},{"id":"https://openalex.org/keywords/hilbert-s-16th-problem","display_name":"Hilbert's 16th problem","score":0.7110000252723694},{"id":"https://openalex.org/keywords/number-of-limit-cycles","display_name":"number of limit cycles","score":0.609000027179718}],"concepts":[{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.8324999809265137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7669000029563904},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7425000071525574},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6725999712944031},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6664000153541565},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5756000280380249},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5428000092506409},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5184000134468079},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5031999945640564},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46939998865127563},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.42480000853538513},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.40560001134872437},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.3910999894142151},{"id":"https://openalex.org/C184175843","wikidata":"https://www.wikidata.org/wiki/Q7191425","display_name":"Piecewise linear manifold","level":3,"score":0.34599998593330383},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.3077999949455261},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2946000099182129},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28459998965263367},{"id":"https://openalex.org/C65092005","wikidata":"https://www.wikidata.org/wiki/Q7885107","display_name":"Uniform limit theorem","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C51337361","wikidata":"https://www.wikidata.org/wiki/Q1825444","display_name":"Limit set","level":3,"score":0.27079999446868896},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08725","pdf_url":"https://arxiv.org/pdf/2610.08725","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.08725","doi":"https://doi.org/10.48550/arxiv.2610.08725","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08725","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.08725","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08725","pdf_url":"https://arxiv.org/pdf/2610.08725","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3187993737","display_name":"Non-smooth Systems and Singular Perturbations","funder_award_id":"ANR-23-CE40-0028","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7080048889","display_name":null,"funder_award_id":"ANR-23","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8182037797","display_name":null,"funder_award_id":"302154/2022-1","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8422559432","display_name":null,"funder_award_id":"2023/02959-5","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220971349.pdf","grobid_xml":"https://content.openalex.org/works/W7220971349.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4395448785","https://openalex.org/W4410601747","https://openalex.org/W7158887397"],"related_works":["https://openalex.org/W4410601747","https://openalex.org/W4402793978","https://openalex.org/W4415654696","https://openalex.org/W2032926717","https://openalex.org/W7158887397","https://openalex.org/W2064732778","https://openalex.org/W2474161785","https://openalex.org/W3127793984","https://openalex.org/W2095526788","https://openalex.org/W4395448785"],"abstract_inverted_index":{"This":[0],"work":[1],"investigates":[2],"the":[3,10,43,51],"number":[4,44],"of":[5,13,39,45,53],"limit":[6,46,57],"cycles":[7,58],"bifurcating":[8],"from":[9],"periodic":[11],"orbits":[12],"a":[14],"linear":[15],"center":[16],"when":[17],"it":[18],"is":[19],"perturbed":[20],"by":[21,29],"piecewise":[22,61],"holomorphic":[23,63],"systems":[24,64],"with":[25],"three":[26],"zones":[27,41],"separated":[28],"two":[30],"external":[31],"circles.":[32],"We":[33],"analyze":[34],"how":[35],"different":[36],"geometric":[37],"configurations":[38],"these":[40],"influence":[42],"cycles.":[47],"Moreover,":[48],"we":[49],"show":[50],"existence":[52],"at":[54],"least":[55],"sixteen":[56],"in":[59],"fourth-degree":[60],"polynomial":[62],"under":[65],"certain":[66],"configurations.":[67]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
