The solution of the Poincaré problem on the rational first integral for the Liénard polynomial differential equations

In this work we classify the polynomial Liénard differential equations ̈ + () ̇ + = 0, having a rational first integral. Such classification was asked by Poincaré in 1891 for any general polynomial differential systems in the plane R2 . As far as we know it is the first time that the complete classi...

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Detalhes bibliográficos
Autores: Giné, Jaume, Llibre, Jaume
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Recursos:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/85165
Acesso em linha:https://doi.org/10.1016/j.chaos.2022.113013
http://hdl.handle.net/10459.1/85165
Access Level:acceso abierto
Palavra-chave:Liénard equation
Rational first integral
Poincaré problem
Polynomial differential equation
Descrição
Resumo:In this work we classify the polynomial Liénard differential equations ̈ + () ̇ + = 0, having a rational first integral. Such classification was asked by Poincaré in 1891 for any general polynomial differential systems in the plane R2 . As far as we know it is the first time that the complete classification is given for a relevant class of polynomial differential equations of arbitrary degree.