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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Detalles Bibliográficos
Autor: Giné, Jaume
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
Descripción
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.