Center Problem and Multiple Hopf bifurcation for the Z5-Equivariant Planar Polynomial Vector Fields of Degree 5

Abstract

This paper proves that a Z5-equivariant planar polynomial vector field of degree 5 has at least five symmetric centers, if and only if it is a Hamltonian vector field. The characterization of a center problem is completely solved. The shortened expressions of the first four Lyapunov constants are given. Under small Z5-equivariant perturbations, the conclusion that the perturbed system has at least 25 limit cycles with the scheme 〈5 5 5 5 5〉 is rigorously proved.

DOI: 10.1142/S0218127409023810

Cite this paper

@article{Liu2009CenterPA, title={Center Problem and Multiple Hopf bifurcation for the Z5-Equivariant Planar Polynomial Vector Fields of Degree 5}, author={Yirong Liu and Jibin Li}, journal={I. J. Bifurcation and Chaos}, year={2009}, volume={19}, pages={2115-2121} }