Journal:
:Annales de l'Institut Henri Poincaré C, Analyse non linéaire2022
Consider the effective Hamiltonian $\overline H(p)$ associated with mechanical $H(p,x)={1\over 2}|p|^2+V(x)$. We prove that for generic $V$, H$ is piecewise 1d in a dense open set two dimensions using Aubry-Mather theory.
