{"id":"https://openalex.org/W2025424184","doi":"https://doi.org/10.1142/s0218127409025195","title":"LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS","display_name":"LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS","publication_year":2009,"publication_date":"2009-11-01","ids":{"openalex":"https://openalex.org/W2025424184","doi":"https://doi.org/10.1142/s0218127409025195","mag":"2025424184"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409025195","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409025195","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101481701","display_name":"Jos\u00e9 Luis Bravo","orcid":"https://orcid.org/0000-0002-0012-7699"},"institutions":[{"id":"https://openalex.org/I80606768","display_name":"Universidad de Extremadura","ror":"https://ror.org/0174shg90","country_code":"ES","type":"education","lineage":["https://openalex.org/I80606768"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J. L. BRAVO","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Extremadura, 06071 Badajoz, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Extremadura, 06071 Badajoz, Spain","institution_ids":["https://openalex.org/I80606768"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100674092","display_name":"Manuel Fern\u00e1ndez","orcid":"https://orcid.org/0000-0002-8035-839X"},"institutions":[{"id":"https://openalex.org/I80606768","display_name":"Universidad de Extremadura","ror":"https://ror.org/0174shg90","country_code":"ES","type":"education","lineage":["https://openalex.org/I80606768"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. FERN\u00c1NDEZ","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad de Extremadura, 06071 Badajoz, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad de Extremadura, 06071 Badajoz, Spain","institution_ids":["https://openalex.org/I80606768"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078018430","display_name":"Armengol Gasull","orcid":"https://orcid.org/0000-0002-1719-8231"},"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":"A. GASULL","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Edifici C, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Edifici C, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain","institution_ids":["https://openalex.org/I123044942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101481701"],"corresponding_institution_ids":["https://openalex.org/I80606768"],"apc_list":null,"apc_paid":null,"fwci":2.3989228,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.88129968,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"19","issue":"11","first_page":"3869","last_page":"3876"},"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":1.0,"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":1.0,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9815000295639038,"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/mathematics","display_name":"Mathematics","score":0.7862445116043091},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.7176173329353333},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6480803489685059},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.5369093418121338},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4957943856716156},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4742366671562195},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45943352580070496},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.4543733298778534},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.42562830448150635},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3422975540161133},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3418247103691101},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2055472731590271},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09127753973007202}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7862445116043091},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.7176173329353333},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6480803489685059},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.5369093418121338},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4957943856716156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4742366671562195},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45943352580070496},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.4543733298778534},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.42562830448150635},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3422975540161133},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3418247103691101},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2055472731590271},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09127753973007202},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127409025195","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409025195","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1511004822","https://openalex.org/W1984301218","https://openalex.org/W2010995477","https://openalex.org/W2012948976","https://openalex.org/W2018087114","https://openalex.org/W2022888790","https://openalex.org/W2025455846","https://openalex.org/W2025458089","https://openalex.org/W2034478771","https://openalex.org/W2042656955","https://openalex.org/W2047361099","https://openalex.org/W2062983822","https://openalex.org/W2117865802","https://openalex.org/W2125797455"],"related_works":["https://openalex.org/W634571496","https://openalex.org/W579400037","https://openalex.org/W2951578208","https://openalex.org/W1570037808","https://openalex.org/W4298173607","https://openalex.org/W4386784405","https://openalex.org/W115184939","https://openalex.org/W4285286257","https://openalex.org/W2153015377","https://openalex.org/W218242978"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"some":[3],"2\u03c0-periodic":[4],"generalized":[5],"Abel":[6,68],"equations":[7],"of":[8,37,47,87],"the":[9,48,53,67,79],"form":[10],"x\u2032":[11,70],"=":[12,71],"A(t)x":[13,72],"n":[14,21],"+":[15,18,74],"B(t)x":[16,75],"m":[17,23,26],"C(t)x,":[19],"with":[20,44],"\u2260":[22],"and":[24,56,82],"n,":[25],"\u2265":[27],"2":[28,76],"have":[29],"at":[30],"most":[31],"three":[32],"limit":[33],"cycles.":[34],"The":[35],"novelty":[36],"our":[38,50],"result":[39],"is":[40],"that,":[41],"in":[42,64],"contrast":[43],"other":[45],"results":[46],"literature,":[49],"hypotheses":[51],"allow":[52],"functions":[54,80],"A,B,":[55],"C":[57],"to":[58],"change":[59],"sign.":[60],"Finally":[61],"we":[62],"study":[63],"more":[65],"detail":[66],"equation":[69],"3":[73],",":[77],"where":[78],"A":[81],"B":[83],"are":[84],"trigonometric":[85],"polynomials":[86],"degree":[88],"one.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}