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 ẍ + f(x) ẋ + x = 0, having a rational first integral. Such classification was asked by Poincaré in 1891 for any general polynomial differential systems in the plane R. As far as we know it is the first time that the complete clas...

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Detalles Bibliográficos
Autores: Giné, Jaume|||0000-0001-7109-2553, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:303173
Acceso en línea:https://ddd.uab.cat/record/303173
https://dx.doi.org/urn:doi:10.1016/j.chaos.2022.113013
Access Level:acceso abierto
Palabra clave:Liénard equation
Rational first integral
Poincaré problem
Polynomial Differential equation
Descripción
Sumario:In this work we classify the polynomial Liénard differential equations ẍ + f(x) ẋ + x = 0, having a rational first integral. Such classification was asked by Poincaré in 1891 for any general polynomial differential systems in the plane R. 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.