Limit Cycles of Discontinuous Piecewise Differential Hamiltonian Systems Separated by a Straight Line
Casimiro, Joyce A. (Universidade Estadual de Campinas (Brasil))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	In this article, we study the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems separated by a straight line. We consider three cases, when both Hamiltonians systems in each side of the discontinuity line have simultaneously degree one, two or three. We obtain that in these three cases, this maximum number is zero, one and three, respectively. Moreover, we prove that there are discontinuous piecewise differential systems realizing these maximum number of limit cycles. Note that we have solved the extension of the 16th Hilbert problem about the maximum number of limit cycles that these three classes of discontinuous piecewise differential systems separated by one straight line and formed by two Hamiltonian systems with a degree either one, two, or three, which such systems can exhibit.
Note:	Fundación de Investigación de São Paulo (FAPESP) 2018/25575-0 y 2022/01375-7
Note:	Agencia Estatal de Investigación beca PID2022-136613NB-100
Note:	European Research Council MSCA-RISE-2017-777911 Beca H2020
Note:	Generalitat de Catalunya beca 2021 SGR 00113 y la Real 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:	Discontinuous piecewise differential systems ; Limit cycle ; Hamiltonian systems
Published in:	Axioms, Vol. 13 Núm. 3 (2024) , p. 1-7, ISSN 2075-1680

DOI: 10.3390/axioms13030161

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