Limit cycles of 3-dimensional discontinuous piecewise differential systems formed by linear centers

In this paper we deal with 3-dimensional discontinuous piecewise differential systems formed by linear centers and separated by one plane or two parallel planes. We prove that these systems separated by one plane have no limit cycles, besides the systems separated by two parallel planes have at most...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, De Moraes, Jaime Rezende|||0000-0002-7722-6644
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:257081
Acceso en línea:https://ddd.uab.cat/record/257081
https://dx.doi.org/urn:doi:10.1007/s40863-021-00237-0
Access Level:acceso abierto
Palabra clave:Discontinuous piecewise differential systems
Periodic orbits
Linear centers
First integrals
Limit cycles
Descripción
Sumario:In this paper we deal with 3-dimensional discontinuous piecewise differential systems formed by linear centers and separated by one plane or two parallel planes. We prove that these systems separated by one plane have no limit cycles, besides the systems separated by two parallel planes have at most one limit cycle, and that there are systems having such a limit cycle. So we solve the extension of the 16th Hilbert problem to this class of differential systems.