Crossing limit cycles for discontinuous piecewise linear differential centers separated by three parallel straight lines
Anacleto, Maria Elisa (Universidad del Bío-Bío. Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)

Date:	2023
Abstract:	In this paper we study the continuous and discontinuous planar piecewise differential systems formed by four linear centers separated by three parallel straight lines denoted by Σ = {(x,y) ∈ R2 : x = -p, x = 0, x = q, p, q > 0}. We prove that when these piecewise differential systems are continuous they have no limit cycles. While for the discontinuous case we show that they can have at most four limit cycles and we also provide examples of such systems with zero, one, and two limit cycles. In particular we have solved the extension of the 16th Hilbert problem to this class of piecewise differential systems.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Linear centers ; Continuous piecewise differential systems ; Discontinuous piecewise differential systems ; First integrals
Published in:	Rendiconti del Circolo Matematico di Palermo, Vol. 72, Issue 3 (April 2023) , p. 1739-1750, ISSN 1973-4409

DOI: 10.1007/s12215-022-00766-3

Postprint 12 p, 317.0 KB

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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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