TY - JOUR
T1 - A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves
AU - Giné, Jaume
AU - Llibre, Jaume
N1 - Publisher Copyright:
© 2022 The Authors
PY - 2022/5
Y1 - 2022/5
N2 - 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. 2010 mathematics subject classification: Primary 34A05. Secondary 34C05, 37C10.
AB - 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. 2010 mathematics subject classification: Primary 34A05. Secondary 34C05, 37C10.
KW - First integrals
KW - Invariant algebraic curve
KW - Liénard polynomial differential systems
UR - https://www.scopus.com/pages/publications/85129318077
U2 - 10.1016/j.chaos.2022.112075
DO - 10.1016/j.chaos.2022.112075
M3 - Article
AN - SCOPUS:85129318077
SN - 0960-0779
VL - 158
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 112075
ER -