The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve y= xn

We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in t...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:299284
Acceso en línea:https://ddd.uab.cat/record/299284
https://dx.doi.org/urn:doi:10.1007/s11040-023-09467-4
Access Level:acceso abierto
Palabra clave:Non-smooth differential system
Limit cycle
Discontinuous piecewise linear differential system
Linear centers
Linear Hamiltonian saddles
Descripción
Sumario:We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in terms of n, proving the extended 16th Hilbert problem in this case. In particular, we show that for n= 2 this bound can be reached.