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

Detalhes bibliográficos
Autor(a) principal: Llibre, Jaume
Data de Publicação: 2021
Outros Autores: Pessoa, Claudio [UNESP], Ribeiro, Jarne D.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1590/0001-3765202120191139
http://hdl.handle.net/11449/229568
Resumo: 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.
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spelling Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equationsLiénard equationPoincaré problemPolinomial differential equationRational first integralPoincaré 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.Federación Española de Enfermedades RarasFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Departament de Matemàtiques Universitat Autònoma de Barcelona, 08193 BellaterraDepartamento de Matemática Universidade Estadual Paulista, Campus São José do Rio Preto, IBILCE, R. Cristóvão Colombo 2265Instituto Federal de Educação Ciência e Tecnologia do Sul de Minas Gerais IFSULDEMINAS, Rua Mario Ribola 409, Penha IIDepartamento de Matemática Universidade Estadual Paulista, Campus São José do Rio Preto, IBILCE, R. Cristóvão Colombo 2265FAPESP: 18/19726-5FAPESP: 19/10269-3CAPES: 88881.068462/2014-01Universitat Autònoma de BarcelonaUniversidade Estadual Paulista (UNESP)IFSULDEMINASLlibre, JaumePessoa, Claudio [UNESP]Ribeiro, Jarne D.2022-04-29T08:33:15Z2022-04-29T08:33:15Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1590/0001-3765202120191139Anais da Academia Brasileira de Ciencias, v. 93, n. 4, 2021.1678-26900001-3765http://hdl.handle.net/11449/22956810.1590/0001-37652021201911392-s2.0-85115401790Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengAnais da Academia Brasileira de Cienciasinfo:eu-repo/semantics/openAccess2022-04-29T08:33:15Zoai:repositorio.unesp.br:11449/229568Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-29T08:33:15Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
title Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
spellingShingle Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
Llibre, Jaume
Liénard equation
Poincaré problem
Polinomial differential equation
Rational first integral
title_short Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
title_full Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
title_fullStr Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
title_full_unstemmed Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
title_sort Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
author Llibre, Jaume
author_facet Llibre, Jaume
Pessoa, Claudio [UNESP]
Ribeiro, Jarne D.
author_role author
author2 Pessoa, Claudio [UNESP]
Ribeiro, Jarne D.
author2_role author
author
dc.contributor.none.fl_str_mv Universitat Autònoma de Barcelona
Universidade Estadual Paulista (UNESP)
IFSULDEMINAS
dc.contributor.author.fl_str_mv Llibre, Jaume
Pessoa, Claudio [UNESP]
Ribeiro, Jarne D.
dc.subject.por.fl_str_mv Liénard equation
Poincaré problem
Polinomial differential equation
Rational first integral
topic Liénard equation
Poincaré problem
Polinomial differential equation
Rational first integral
description 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.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
2022-04-29T08:33:15Z
2022-04-29T08:33:15Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1590/0001-3765202120191139
Anais da Academia Brasileira de Ciencias, v. 93, n. 4, 2021.
1678-2690
0001-3765
http://hdl.handle.net/11449/229568
10.1590/0001-3765202120191139
2-s2.0-85115401790
url http://dx.doi.org/10.1590/0001-3765202120191139
http://hdl.handle.net/11449/229568
identifier_str_mv Anais da Academia Brasileira de Ciencias, v. 93, n. 4, 2021.
1678-2690
0001-3765
10.1590/0001-3765202120191139
2-s2.0-85115401790
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Anais da Academia Brasileira de Ciencias
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1799965627965767680

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