Abstract

We study four parameter unfoldings $X$_λ of symmetric elliptic Hamiltonians of degree four. We prove that in a compact region of the period annulus of $X$₀ the displacement function of $X$_λ is sign equivalent to its principal part. This principal part is a family induced by a Chebyshev system. We hence describe the behavior of $X$_λ, for the parameter $\lambda$ in a full neighborhood of the origin.

This is a joint work with Chengzhi Li and Robert Roussarie.