Reversible global centres with quintic homogeneous nonlinearities
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Date:	2023
Abstract:	A center of a differential system in the plane R2 is an equilibrium point p having a neighbourhood U such that U \ {p} is filled of periodic orbits. A global center is a center p such that R2 \ {p} is filled of periodic orbits. To determine when a given differential system has a center is in general a difficult problem, but to determine if a given differential system has a global center is even more difficult. We deal with the class of polynomial differential systems of the form (1) ˙x = -y + P(x, y), y˙ = x + Q(x, y), with P and Q homogeneous polynomials of degree n. It is known that these systems only can have global centers if n is odd. The global centers when n is 1 or 3 have been characterized. Here for n = 5 we classify the global centers of a four parameter family of systems (1). In particular we illustrate how to study the local phase portraits of the singular points whose linear part is identically zero using only vertical blow ups.
Grants:	European Commission 777911 Agencia Estatal de Investigación PID2019-104658GB-I00
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Center ; Global center ; Polynomial differential systems
Published in:	Dynamical Systems, Vol. 38, Issue 4 (July 2023) , p. 632-653, ISSN 1468-9375

DOI: 10.1080/14689367.2023.2228737

Postprint 27 p, 1.1 MB

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