Consider the effective Hamiltonian associated with the mechanical Hamiltonian . We prove that for generic , is piecewise one-dimensional in a dense open set in two dimensions using Aubry–Mather theory.
Cite this article
Yifeng Yu, High degeneracy of effective Hamiltonian in two dimensions. Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), no. 1, pp. 201–223DOI 10.4171/AIHPC/6