The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems

In order to understand the dynamics of the planar differential systems, the limit cycles play a main role, but in general their study is not easy. These last years, an increasing interest appeared for studying the limit cycles of some classes of piecewise differential systems, due to the rich applic...

ver descrição completa

Detalhes bibliográficos
Autores: Barkat, Meriem, Benterki, Rebiha|||0000-0001-6745-2747, Llibre, Jaume|||0000-0002-9511-5999
Formato: artículo
Fecha de publicación:2023
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:274779
Acesso em linha:https://ddd.uab.cat/record/274779
https://dx.doi.org/urn:doi:10.1007/s11071-022-07891-9
Access Level:acceso abierto
Palavra-chave:Limit cycle
Discontinuous piecewise linear differential systems
Linear differential center
Hamiltonian isochronous global center
Descrição
Resumo:In order to understand the dynamics of the planar differential systems, the limit cycles play a main role, but in general their study is not easy. These last years, an increasing interest appeared for studying the limit cycles of some classes of piecewise differential systems, due to the rich applications of this kind of differential systems. This paper solves the extended 16th Hilbert problem for a family of discontinuous planar differential systems with two regions separated by the straight line x= 0. By using the first integrals, we prove that the maximum number of crossing limit cycles in the family of systems formed by a linear center and a class of Hamiltonian isochronous global center with a polynomial first integral of degree 2n is 5.