Limit cycles for some families of smooth and non-smooth planar systems - Buzzi, Claudio A. [UNESP]; Romano Carvalho, Yagor [UNESP]; Gasull, Armengol (Elsevier B.V., 2021)
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 Sigma = {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. (C) 2021 Elsevier Ltd. All rights reserved.
Keywords: Limit cycles; First order averaging; Extended complete Chebyshev systems; Hilbert numbers