The Extended 16th Hilbert Problem for Discontinuous Piecewise Systems Formed by Linear Centers and Linear Hamiltonian Saddles Separated by a Nonregular Line
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Additional title:	The extended 16-th Hilbert problem for discontinuous piecewise systems formed by linear centers and linear Hamiltonian saddles separated by a non-regular line
Date:	2023
Abstract:	We study discontinuous piecewise linear differential systems formed by linear centers and/or linear Hamiltonian saddles and separated by a nonregular straight line. There are two classes of limit cycles: the ones that intersect the separation line at two points and the ones that intersect the separation line in four points, named limit cycles of type II2 and limit cycles of type II4, respectively. We prove that the maximum numbers of limit cycles of types II2 and II4 are two and one, respectively. We show that all these upper bounds are reached providing explicit examples.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2022/SGR-00113
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, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Piecewise linear differential systems ; Discontinuity nonregular line ; Limit cycles
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 16 (December 2023) , art. 2350196, ISSN 1793-6551

DOI: 10.1142/S0218127423501961

Postprint 10 p, 485.5 KB

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