Limit cycles of planar discontinuous piecewise linear Hamiltonian systems in three regions of Y-type
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação)

Date:	2026
Abstract:	In recent years there has been a significant interest in studying discontinuous piecewise differential systems, mainly due to the wide range of applications in modeling natural phenomena. To understand the dynamics of these systems in the plane one challenge is to control their number of limit cycles. In this paper we study the existence of limit cycles in planar discontinuous piecewise linear Hamiltonian systems with three zones separated by the line Y = {(x,y) : x ≥ 0 and y = 0} ∪ {(x,y) : x = 0 and y ≥ 0} ∪ {(x,y) : x ≤ 0 and y = 0}. We provide the maximum number of crossing limit cycles intersecting each branch of Y in one point, and intersecting two branches of the Y each one in two points. So we have solved the extension of the 16th Hilbert problem to this class of differential systems.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Generalitat de Catalunya 2021/SGR-00113 European Commission 101183111
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
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 publicada
Subject:	Crossing limit cycle ; Linear Hamiltonian system ; Discontinuous piecewise differential system
Published in:	Chaos, solitons and fractals, Vol. 207 (June 2026) , art. 117997, ISSN 0960-0779

DOI: 10.1016/j.chaos.2026.117997

8 p, 752.9 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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