Home > Articles > Published articles > Characterization of the kukles polynomial differential systems having an invariant algebraic curve |
Date: | 2023 |
Abstract: | Let f(x) and g(x) be complex polynomials. We characterize all Kukles polynomial differential systems of the form x = y, y = −y −f(x)y −g(x) having an invariant algebraic curve. We show that expanding an invariant algebraic curve of these differential systems as a polynomial in the variable y, the first four higher coefficients of the polynomial defining the invariant algebraic curve determine completely these Kukles systems. In particular if the second and third higher coefficients of the polynomial defining the invariant algebraic curve satisfy a simple relation between them the invariant algebraic curve is of the form (y + p(x)) = 0 for some polynomial p(x) and y + p(x) = 0 is an invariant algebraic curve of the Kukles system for any complex polynomial f(x). |
Grants: | Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 |
Rights: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Kukles polynomial differential systems ; Invariant algebraic curve |
Published in: | Bulletin des Sciences Mathematiques, Vol. 182 (February 2023) , art. 103224, ISSN 0007-4497 |
Available from: 2025-02-28 Postprint |