High degeneracy of effective Hamiltonian in two dimensions

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE（2022）

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摘要

Consider the effective Hamiltonian (H) over bar (p) associated with the mechanical Hamiltonian H(p, x) = 1/2 vertical bar p vertical bar(2) + V(x). We prove that for generic V, (H) over bar is piecewise one-dimensional in a dense open set in two dimensions using Aubry-Mather theory.

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关键词

Homogenization, effective Hamiltonian, Aubry-Mather theory, weak KAM theory

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