Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by nonregular curves

The problem of determining the existence, maximum number and positions of the limit cycles of the planar discontinuous piecewise linear differential systems is an important problem in the qualitative theory of differential systems. In this paper, we study two families of piecewise linear Hamiltonian...

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Detalles Bibliográficos
Autores: Jimenez Ruiz, Jeidy Johana|||0000-0002-3378-4679, Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:268646
Acceso en línea:https://ddd.uab.cat/record/268646
https://dx.doi.org/urn:doi:10.1142/S021812742250184X
Access Level:acceso abierto
Palabra clave:Crossing limit cycle
Discontinuous piecewise linear Hamiltonian system
Nonregular curve
Descripción
Sumario:The problem of determining the existence, maximum number and positions of the limit cycles of the planar discontinuous piecewise linear differential systems is an important problem in the qualitative theory of differential systems. In this paper, we study two families of piecewise linear Hamiltonian systems without equilibria in R2 separated by a nonregular curve. We provide the maximum number of crossing limit cycles that each family can have and show when this maximum is reached. In this way we are solving for each family the extended 16th Hilbert problem.