## Center problem and multiple Hopf bifurcation

- Y. R. Liu, J. B. Li
- 2009

2 Excerpts

- Published 2009 in I. J. Bifurcation and Chaos

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.

@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}
}