Abstract:

In this talk, we will introduce a bound on the number of limit cycles bifurcating from the period annulus of quasi-homogeneous Hamiltonian systems at any order of Melnikov functions. The explicit expression of this bound is given in terms of $(n,k,s_1,s_2)$, where $n$ is the degree of perturbation polynomials, $k$ is the order of the first nonzero higher order Melnikov function, and $(s_1,s_2)$ is the weight exponent of quasi-homogeneous Hamiltonian with center.

This is based on a joint work with Jean-Pierre Françoise and Hongjin He.

Slides of the talk.