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