Invariant algebraic curves for certain generalized Liénard differential system
In this work we solve the problem of finding the invariant algebraic curves of a generalized Li´enard differential system ˙x = y, ˙y = −f(x)y − g(x), where deg f = m and deg g = n and with n = m + 1, generalizing the known previous examples. In particular it is studied the case m = 3 and n = 4. The...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/464749 |
| Acceso en línea: | https://doi.org/10.3934/cpaa.2022159 https://hdl.handle.net/10459.1/464749 |
| Access Level: | acceso abierto |
| Palabra clave: | Liénard systems Invariant algebraic curves Darboux polynomials Puiseux series |
| Sumario: | In this work we solve the problem of finding the invariant algebraic curves of a generalized Li´enard differential system ˙x = y, ˙y = −f(x)y − g(x), where deg f = m and deg g = n and with n = m + 1, generalizing the known previous examples. In particular it is studied the case m = 3 and n = 4. The difficulties in applying the Puiseux method are shown even when the degrees of the invariant curves are bounded. |
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