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...
| Autores: | , |
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| 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 |
| 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. |
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