Limit cycles for some families of smooth and non-smooth planar systems
Buzzi, Claudio (Universidade Estadual Paulista Julio de Mesquita Filho. Mathematics Department (Brazil))
Carvalho, Yagor Romano (Universidade Estadual Paulista Julio de Mesquita Filho. Mathematics Department (Brazil))
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
Abstract:	We apply the averaging method in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our results can be applied to models where the smoothness is lost on the set Σ = {xy = 0}. They also motivate to consider a variant of Hilbert 16th problem, where the goal is to bound the number of limit cycles in terms of the number of monomials of a family of polynomial vector fields, instead of doing this in terms of their degrees.
Grants:	Ministerio de Ciencia e Innovación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; First order averaging ; Extended complete Chebyshev systems ; Hilbert numbers
Published in:	Nonlinear Analysis : Theory, Methods and Applications, Vol. 207 (June 2021) , p. 112298, ISSN 0362-546X

DOI: 10.1016/j.na.2021.112298

Postprint 13 p, 345.6 KB

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