Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres
Buzzi, Claudio (Universidade Estadual Paulista Julio de Mesquita Filho. Departamento de Matemática)
Carvalho, Yagor Romano (Universidade de São Paulo. Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2022
Abstract:	These last years an increasing interest appeared in studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. The understanding of the dynamics of these systems has many difficulties. One of them is the study of their limit cycles. In this paper, we study the maximum number of crossing limit cycles of some classes of planar discontinuous piecewise differential systems separated by a straight line and formed by combinations of linear centres (consequently isochronous) and cubic isochronous centres with homogeneous nonlinearities. For these classes of planar discontinuous piecewise differential systems we solved the extension of the 16th Hilbert problem, i. e. we provide an upper bound for their maximum number of crossing limit cycles.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Linear centres ; Cubic isochronous centres with homogeneous nonlinearities ; Discontinuous piecewise differential systems ; First integrals
Published in:	Dynamical Systems, Vol. 37, Issue 4 (2022) , p. 710-728, ISSN 1468-9375

DOI: 10.1080/14689367.2022.2122779

Postprint 17 p, 375.4 KB

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