Limit cycles of 3-dimensional discontinuous piecewise differential systems formed by linear centers
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
De Moraes, Jaime Rezende (Universidade Estadual do Mato Grosso do Sul - Rodovia Dourados. Curso de Matemática)

Date:	2021
Abstract:	In this paper we deal with 3-dimensional discontinuous piecewise differential systems formed by linear centers and separated by one plane or two parallel planes. We prove that these systems separated by one plane have no limit cycles, besides the systems separated by two parallel planes have at most one limit cycle, and that there are systems having such a limit cycle. So we solve the extension of the 16th Hilbert problem to this class of differential systems.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Discontinuous piecewise differential systems ; Periodic orbits ; Linear centers ; First integrals ; Limit cycles
Published in:	São Paulo Journal of Mathematical Sciences, Vol. 15, Issue 2 (December 2021) , p. 858-874, ISSN 2316-9028

DOI: 10.1007/s40863-021-00237-0

Postprint 15 p, 714.9 KB

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