Semi-discrete approximations converge in the Kuratowski sense to continuous Aubry and Mather sets, with full convergence under hyperbolicity for Aubry sets and finite ergodic measures for Mather sets.
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Semi-Discrete Approximation of Aubry and Mather sets
Semi-discrete approximations converge in the Kuratowski sense to continuous Aubry and Mather sets, with full convergence under hyperbolicity for Aubry sets and finite ergodic measures for Mather sets.