Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
dc.contributor.author | Llibre, Jaume | |
dc.contributor.author | Pessoa, Claudio [UNESP] | |
dc.contributor.author | Ribeiro, Jarne D. | |
dc.contributor.institution | Universitat Autònoma de Barcelona | |
dc.contributor.institution | Universidade Estadual Paulista (UNESP) | |
dc.contributor.institution | IFSULDEMINAS | |
dc.date.accessioned | 2022-04-29T08:33:15Z | |
dc.date.available | 2022-04-29T08:33:15Z | |
dc.date.issued | 2021-01-01 | |
dc.description.abstract | Poincaré 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.affiliation | Departament de Matemàtiques Universitat Autònoma de Barcelona, 08193 Bellaterra | |
dc.description.affiliation | Departamento de Matemática Universidade Estadual Paulista, Campus São José do Rio Preto, IBILCE, R. Cristóvão Colombo 2265 | |
dc.description.affiliation | Instituto Federal de Educação Ciência e Tecnologia do Sul de Minas Gerais IFSULDEMINAS, Rua Mario Ribola 409, Penha II | |
dc.description.affiliationUnesp | Departamento de Matemática Universidade Estadual Paulista, Campus São José do Rio Preto, IBILCE, R. Cristóvão Colombo 2265 | |
dc.description.sponsorship | Federación Española de Enfermedades Raras | |
dc.description.sponsorship | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | |
dc.description.sponsorship | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) | |
dc.description.sponsorshipId | FAPESP: 18/19726-5 | |
dc.description.sponsorshipId | FAPESP: 19/10269-3 | |
dc.description.sponsorshipId | CAPES: 88881.068462/2014-01 | |
dc.identifier | http://dx.doi.org/10.1590/0001-3765202120191139 | |
dc.identifier.citation | Anais da Academia Brasileira de Ciencias, v. 93, n. 4, 2021. | |
dc.identifier.doi | 10.1590/0001-3765202120191139 | |
dc.identifier.issn | 1678-2690 | |
dc.identifier.issn | 0001-3765 | |
dc.identifier.scopus | 2-s2.0-85115401790 | |
dc.identifier.uri | http://hdl.handle.net/11449/229568 | |
dc.language.iso | eng | |
dc.relation.ispartof | Anais da Academia Brasileira de Ciencias | |
dc.source | Scopus | |
dc.subject | Liénard equation | |
dc.subject | Poincaré problem | |
dc.subject | Polinomial differential equation | |
dc.subject | Rational first integral | |
dc.title | Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations | en |
dc.type | Artigo | |
unesp.author.orcid | 0000-0002-9511-5999[1] | |
unesp.author.orcid | 0000-0001-6790-1055[2] | |
unesp.author.orcid | 0000-0001-9729-900X[3] | |
unesp.campus | Universidade Estadual Paulista (Unesp), Instituto de Biociências, Letras e Ciências Exatas, São José do Rio Preto | pt |
unesp.department | Matemática - IBILCE | pt |