An extension of the 16th Hilbert problem for continuous piecewise linear-quadratic centers separated by a non-regular line
Esteban, Marina (Universidad de Córdoba. Departamento de Informática y Análisis Numérico)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento Matemática)

Date:	2023
Abstract:	In the last few decades, there has been much interest in studying piecewise differential systems. This is mainly due to the fact that these differential systems allow us to modelize many natural phenomena. In order to describe the dynamics of a differential system, we need to control its periodic orbits and, especially, its limit cycles. In particular, providing an upper bound for the maximum number of limit cycles that such differential systems can exhibit would be desirable, that is solving the extended 16th Hilbert problem. In general, this is an unsolved problem. In this paper, we give an upper bound for the maximum number of limit cycles that a class of continuous piecewise differential systems formed by an arbitrary linear center and an arbitrary quadratic center separated by a non-regular line can exhibit. So for this class of continuous piecewise differential systems, we have solved the extended 16th Hilbert problem, and the upper bound found is seven. The question whether this upper bound is sharp remains open.
Grants:	Agencia Estatal de Investigación PID2021-123200NB-I00 Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Nonlinear systems ; Periodic-orbit theory ; Phase space methods ; Functions and mappings
Published in:	Chaos, Vol. 33, Issue 12 (December 2023) , art. 123120, ISSN 1089-7682

DOI: 10.1063/5.0167089

Postprint 19 p, 300.3 KB

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