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...

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Detalles Bibliográficos
Autores: Giné, Jaume, Llibre, Jaume
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
Descripción
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.