TY - JOUR
T1 - Limit cycles for some families of smooth and non-smooth planar systems
AU - Buzzi, Claudio
AU - Carvalho, Yagor Romano
AU - Gasull, Armengol
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Limit cycles
KW - First order averaging
KW - Extended complete Chebyshev systems
KW - Hilbert numbers
UR - https://www.scopus.com/pages/publications/85100668194
U2 - 10.1016/j.na.2021.112298
DO - 10.1016/j.na.2021.112298
M3 - Article
SN - 0362-546X
VL - 207
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -