Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations

dc.contributor.authorLlibre, Jaume
dc.contributor.authorPessoa, Claudio [UNESP]
dc.contributor.authorRibeiro, Jarne D.
dc.contributor.institutionUniversitat Autònoma de Barcelona
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.contributor.institutionIFSULDEMINAS
dc.date.accessioned2022-04-29T08:33:15Z
dc.date.available2022-04-29T08:33:15Z
dc.date.issued2021-01-01
dc.description.abstractPoincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of Liénard differential equations ẍ + f (x)ẋ + x = 0, being f (x) a polynomial of arbitrary degree. As far as we know it is the first time that all rational first integrals of a relevant class of polynomial differential equations of arbitrary degree has been classified.en
dc.description.affiliationDepartament de Matemàtiques Universitat Autònoma de Barcelona, 08193 Bellaterra
dc.description.affiliationDepartamento de Matemática Universidade Estadual Paulista, Campus São José do Rio Preto, IBILCE, R. Cristóvão Colombo 2265
dc.description.affiliationInstituto Federal de Educação Ciência e Tecnologia do Sul de Minas Gerais IFSULDEMINAS, Rua Mario Ribola 409, Penha II
dc.description.affiliationUnespDepartamento de Matemática Universidade Estadual Paulista, Campus São José do Rio Preto, IBILCE, R. Cristóvão Colombo 2265
dc.description.sponsorshipFederación Española de Enfermedades Raras
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipIdFAPESP: 18/19726-5
dc.description.sponsorshipIdFAPESP: 19/10269-3
dc.description.sponsorshipIdCAPES: 88881.068462/2014-01
dc.identifierhttp://dx.doi.org/10.1590/0001-3765202120191139
dc.identifier.citationAnais da Academia Brasileira de Ciencias, v. 93, n. 4, 2021.
dc.identifier.doi10.1590/0001-3765202120191139
dc.identifier.issn1678-2690
dc.identifier.issn0001-3765
dc.identifier.scopus2-s2.0-85115401790
dc.identifier.urihttp://hdl.handle.net/11449/229568
dc.language.isoeng
dc.relation.ispartofAnais da Academia Brasileira de Ciencias
dc.sourceScopus
dc.subjectLiénard equation
dc.subjectPoincaré problem
dc.subjectPolinomial differential equation
dc.subjectRational first integral
dc.titleRational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equationsen
dc.typeArtigo
unesp.author.orcid0000-0002-9511-5999[1]
unesp.author.orcid0000-0001-6790-1055[2]
unesp.author.orcid0000-0001-9729-900X[3]
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências, Letras e Ciências Exatas, São José do Rio Pretopt
unesp.departmentMatemática - IBILCEpt

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