{"id":"https://openalex.org/W7221962067","doi":"https://doi.org/10.48550/arxiv.2610.19340","title":"Uniqueness of Limit Cycles for Abel Equations and Planar Systems","display_name":"Uniqueness of Limit Cycles for Abel Equations and Planar Systems","publication_year":2026,"publication_date":"2026-10-14","ids":{"openalex":"https://openalex.org/W7221962067","doi":"https://doi.org/10.48550/arxiv.2610.19340"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.19340","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19340","pdf_url":"https://arxiv.org/pdf/2610.19340","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/2610.19340","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158829027","display_name":"Jos\u00e9 Luis Bravo Trinidad","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Trinidad, Jos\u00e9 Luis Bravo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113246712","display_name":"Renhao Tian","orcid":"https://orcid.org/0009-0006-7143-2910","observed_orcids":["https://orcid.org/0009-0006-7143-2910"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tian, Renhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5158778627","display_name":"Yulin Zhao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Yulin","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":0.9994999766349792,"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":0.9994999766349792,"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":0.00019999999494757503,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":9.999999747378752e-05,"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/abel-equation","display_name":"Abel integral equation","score":0.8140000104904175},{"id":"https://openalex.org/keywords/limit-cycles","display_name":"limit cycles","score":0.8389999866485596},{"id":"https://openalex.org/keywords/uniqueness-of-limit-cycles","display_name":"uniqueness of limit cycles","score":0.984000027179718},{"id":"https://openalex.org/keywords/planar-polynomial-systems","display_name":"planar polynomial systems","score":0.8159999847412109},{"id":"https://openalex.org/keywords/quadratic-systems","display_name":"quadratic systems","score":0.8949999809265137},{"id":"https://openalex.org/keywords/hyperbolic-limit-cycles","display_name":"hyperbolic limit cycles","score":0.9010000228881836}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8562999963760376},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8209999799728394},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.8154000043869019},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6176000237464905},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6168000102043152},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5949000120162964},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5867000222206116},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5784000158309937},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4968000054359436},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3862999975681305},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.28029999136924744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2700999975204468}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.19340","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19340","pdf_url":"https://arxiv.org/pdf/2610.19340","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.2610.19340","doi":"https://doi.org/10.48550/arxiv.2610.19340","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.19340","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.19340","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19340","pdf_url":"https://arxiv.org/pdf/2610.19340","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/G2749646526","display_name":null,"funder_award_id":"12371183","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3101893475","display_name":null,"funder_award_id":"124B2006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G410571670","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G451917667","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G4597869349","display_name":null,"funder_award_id":"GR24042","funder_id":"https://openalex.org/F4320328352","funder_display_name":"Junta de Extremadura"},{"id":"https://openalex.org/G5539308778","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G5967599077","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G7301412885","display_name":null,"funder_award_id":"PID2023-151974NB-I00","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320328352","display_name":"Junta de Extremadura","ror":"https://ror.org/01df4mv68"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221962067.pdf","grobid_xml":"https://content.openalex.org/works/W7221962067.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2733850088","https://openalex.org/W2001342449","https://openalex.org/W4377082729","https://openalex.org/W2747686892","https://openalex.org/W3086806404","https://openalex.org/W1993656094","https://openalex.org/W2062983822","https://openalex.org/W3122719515","https://openalex.org/W1989482876","https://openalex.org/W7126245731"],"abstract_inverted_index":{"We":[0],"study":[1],"positive":[2,36],"limit":[3,37,43,81,109],"cycles":[4,110],"of":[5,55,69,95],"the":[6,30,89,112,121],"Abel":[7,64],"equation":[8,31],"$$\\dot{x}=A(t)x^{3}+B(t)x^{2},$$":[9],"where":[10],"$A$":[11],"and":[12,114],"$B$":[13],"are":[14],"$2\u03c0$-periodic":[15],"functions.":[16],"By":[17],"developing":[18],"a":[19,25,42,67,85,104],"half-period":[20],"convexity":[21],"method,":[22],"we":[23,51,73,102],"establish":[24],"new":[26,105],"criterion":[27,107,122],"ensuring":[28],"that":[29,59,75],"has":[32],"at":[33,78],"most":[34,79],"one":[35,80],"cycle.":[38],"Moreover,":[39],"if":[40],"such":[41],"cycle":[44],"exists,":[45],"it":[46],"is":[47,77,123],"hyperbolic.":[48],"As":[49],"applications,":[50],"consider":[52],"two":[53],"classes":[54],"planar":[56],"polynomial":[57],"systems":[58],"can":[60],"be":[61],"reduced":[62],"to":[63,88],"equations.":[65],"For":[66,99],"subfamily":[68],"cubic":[70],"rigid":[71],"systems,":[72,101],"prove":[74],"there":[76],"cycle,":[82],"thereby":[83],"giving":[84],"partial":[86],"answer":[87],"first":[90],"problem":[91],"in":[92],"Gasull's":[93],"list":[94],"33":[96],"open":[97],"problems.":[98],"quadratic":[100],"derive":[103],"uniqueness":[106],"for":[108],"surrounding":[111],"origin":[113],"provide":[115],"explicit":[116],"parameter":[117],"regions":[118],"under":[119],"which":[120],"satisfied.":[124]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-16T00:00:00"}