Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2023
Abstract:	Due to their applications to many physical phenomena during these last decades the interest for studying the continuous or discontinuous piecewise differential systems has increased strongly. The limit cycles play a main role in the study of any planar differential system. Up to now the major part of papers which study the limit cycles of the planar piecewise differential systems have considered systems formed by two pieces separated by one straight line. Here we consider planar continuous piecewise differential systems separated by a parabola. We prove that the planar continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center have at most one limit cycle. Moreover there are systems in this class exhibiting one limit cycle. So in particular we have solved the extension of the 16th Hilbert problem to this class of differential systems.
Grants:	Agencia Estatal de Investigación MTM2016-77278-P Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Continuous piecewise differential system ; Limit cycle ; Linear center ; Quadratic center
Published in:	Discrete and continuous dynamical systems. Series S, Vol. 16, Issue 3-4 (March-April 2023) , p. 533-547, ISSN 1937-1179

DOI: 10.3934/dcdss.2022034

Postprint 12 p, 805.3 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles