Limit cycles for a class of quintic $\mathbb{Z}_6-$equivariant systems without infinite critical points
Dynamical Systems
2014-10-30 v4
Abstract
We analyze the dynamics of a 4-parameter family of planar ordinary differential equations, given by a polynomial of degree 5 that is equivariant under a symmetry of order 6. We obtain the number of limit cycles as a function of the parameters, and provide criteria for proving in some cases uniqueness and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical points, the origin being always one of these points. The method used is the reduction of the problem to an Abel equation.
Keywords
Cite
@article{arxiv.1309.5346,
title = {Limit cycles for a class of quintic $\mathbb{Z}_6-$equivariant systems without infinite critical points},
author = {Maria Jesus Álvarez and Isabel Salgado Labouriau and Adrian Calin Murza},
journal= {arXiv preprint arXiv:1309.5346},
year = {2014}
}