A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves
The generalized Liénard polynomial differential systems are the differential systems of the form x′ = y, y′ = − f(x)y − g(x), where f and g are polynomials. We characterize all the generalized Liénard polynomial differential systems having an invariant algebraic curve. We show that the first four hi...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/84042 |
| Acceso en línea: | https://doi.org/10.1016/j.chaos.2022.112075 http://hdl.handle.net/10459.1/84042 |
| Access Level: | acceso abierto |
| Palabra clave: | Liénard polynomial differential systems Invariant algebraic curve First integrals |
| Sumario: | The generalized Liénard polynomial differential systems are the differential systems of the form x′ = y, y′ = − f(x)y − g(x), where f and g are polynomials. We characterize all the generalized Liénard polynomial differential systems having an invariant algebraic curve. We show that the first four higher coefficients of the polynomial in the variable y, defining the invariant algebraic curve, determine completely the generalized Liénard polynomial differential system. This fact does not hold for arbitrary polynomial differential systems. |
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