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, RIBEIRO,JARNE D.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000700303
Resumo: 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 x ¨ + f ( x ) x ˙ + 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 equationrational first integralPoincaré problempolinomial differential equationAbstract 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 x ¨ + f ( x ) x ˙ + 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.Academia Brasileira de Ciências2021-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000700303Anais da Academia Brasileira de Ciências v.93 n.4 2021reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/0001-3765202120191139info:eu-repo/semantics/openAccessLLIBRE,JAUMEPESSOA,CLAUDIORIBEIRO,JARNE D.eng2021-09-15T00:00:00Zoai:scielo:S0001-37652021000700303Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2021-09-15T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)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
rational first integral
Poincaré problem
polinomial differential equation
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
RIBEIRO,JARNE D.
author_role author
author2 PESSOA,CLAUDIO
RIBEIRO,JARNE D.
author2_role author
author
dc.contributor.author.fl_str_mv LLIBRE,JAUME
PESSOA,CLAUDIO
RIBEIRO,JARNE D.
dc.subject.por.fl_str_mv Liénard equation
rational first integral
Poincaré problem
polinomial differential equation
topic Liénard equation
rational first integral
Poincaré problem
polinomial differential equation
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 x ¨ + f ( x ) x ˙ + 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
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000700303
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000700303
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0001-3765202120191139
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.93 n.4 2021
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
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instname_str Academia Brasileira de Ciências (ABC)
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institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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