Characterization of the kukles polynomial differential systems having an invariant algebraic curve
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)

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

DOI: 10.1016/j.bulsci.2022.103224

Available from: 2025-02-28 Postprint

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles