Limit cycles in 4-star-symmetric planar piecewise linear systems
Buzzi, Claudio (Universidade Estadual Paulista. Departamento de Matemática (Brazil))
Medrado, Joao Carlos (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil))
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2020
Abstract:	Our interest is centered in the study of the number of limit cycles for nonsmooth piecewise linear vector fields on the plane when the switching curve is xy=0. We consider the symmetric case. That is, one vector field defined in the odd quadrants and the other in the even ones. We deal with equilibrium points of center-focus type, with matrices in real Jordan form, in each vector field when the infinity is monodromic. In this case, we provide the center classification at infinity, we prove that the maximum order of a weak focus is five. Moreover, we show the existence of systems exhibiting five limit cycles bifurcating from infinity.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Non-smooth differential system ; 4-cross-symmetric ; Cyclicity ; Limit cycles ; Center-focus problem
Published in:	Journal of differential equations, Vol. 268, Issue 5 (February 2020) , p. 2414-2434, ISSN 1090-2732

DOI: 10.1016/j.jde.2019.09.008

Postprint 19 p, 441.0 KB

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