2026-04-17T22:58:13Zhttps://recercat.cat/oai/request

oai:recercat.cat:10459.1/840422024-12-05T22:05:14Zcom_2072_3622col_2072_479130

00925njm 22002777a 4500 dc Giné, Jaume author Llibre, Jaume author 2022-11-02T09:57:55Z 2022-11-02T09:57:55Z 2022 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. The author is partially supported by the Agencia Estatal de Investigación grant PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2017SGR 1276. The second author is partially supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00, and the H2020 European Research Council grant MSCA-RISE-2017-777911. http://hdl.handle.net/10459.1/84042 Liénard polynomial differential systems Invariant algebraic curve First integrals A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves