Limit cycles for piecewise hybrid polynomial Hamiltonian differential systems
Rodrigues de Lima, Camila A.B. (Universidade Federal de Santa Catarina. Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Additional title:	Limit cycles for piecewise hybrid Hamiltonian differential systems
Date:	2025
Abstract:	In this work we study a class of hybrid differential systems formed by two polynomial Hamiltonian systems separated by a straight line, which we named piecewise hybrid polynomial Hamiltonian systems. We investigate an upper bound for the maximum number of limit cycles that these piecewise hybrid polynomial Hamiltonian systems can exhibit when they have finitely many periodic solutions. Moreover we present some examples where this upper bound is reached. In other words we solve the extension of the 16th Hilbert problem to this class of hybrid differential systems.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Generalitat de Catalunya 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Piecewise hybrid polynomial Hamiltonian systems ; Limit cycles ; Stability analysis
Published in:	São Paulo Journal of Mathematical Sciences, Vol. 19, Num. 2 (December 2025) , art. 34, ISSN 2316-9028

DOI: 10.1007/s40863-025-00513-3

Available from: 2026-12-31 Postprint 9 p, 285.6 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
Articles > Published articles