High Degeneracy of Effective Hamiltonian in Two Dimensions

preprint2020arXivOpen access

Consider the effective Hamiltonian $\overline H(p)$ associated with the mechanical Hamiltonian $H(p,x)={1\over 2}|p|^2+V(x)$ . We prove that for generic $V$ , $\overline H$ is piecewise 1d in a dense open set in two dimensions using Aubry-Mather theory.

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High Degeneracy of Effective Hamiltonian in Two Dimensions

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