Limit Cycles of Continuous-Discontinuous Piecewise Linear Hamiltonian Systems in ℝ2 Separated by the Curve y=sinx
Chachapoyas, N. (Universidade Federal de Itajubá. Instituto de Matemática e Computação)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Meza-Sarmiento, I. S. (Universidade Federal de Itajubá. Instituto de Matemática e Computação)
Vidarte, J. (Universidade Federal de Itajubá. Instituto de Matemática e Computação)

Date:	2026
Abstract:	These last decades piecewise differential systems have been studied intensively, mainly due to their applications. Inside the study of the dynamics of these differential systems, the limit cycles, that is, the isolated periodic orbits inside the set of all periodic orbits of the system, play a main role. We consider continuous-discontinuous piecewise differential systems in the plane (Formula presented. ) separated by the analytic curve (Formula presented. ) and formed by two arbitrary linear Hamiltonian systems: continuous in the sense that the first component of the two Hamiltonian systems coincide on the curve (Formula presented. ) and discontinuous in the sense that the second component of the two Hamiltonian systems are distinct on the curve (Formula presented. ). We prove that such piecewise differential systems can have four limit cycles.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00
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:	Limit cycles ; Piecewise differential systems
Published in:	Mathematical methods in the applied sciences, Vol. 49, Num. 3 (February 2026) , p. 2093-2097, ISSN 1099-1476

DOI: 10.1002/mma.70230

5 p, 1.7 MB

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