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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Bibliographic Details
Authors: Giné, Jaume, Llibre, Jaume
Format: article
Status:Published version
Publication Date:2022
Country:España
Institution:Universitat de Lleida (UdL)
Repository:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/84042
Online Access:https://doi.org/10.1016/j.chaos.2022.112075
http://hdl.handle.net/10459.1/84042
Access Level:Open access
Keyword:Liénard polynomial differential systems
Invariant algebraic curve
First integrals
Description
Summary: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.