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math.DS2026
A Fully Discrete Variational Approximation of Mather Measures and Sets
Fabio Camilli, Cristian Mendico
We introduce a fully--discrete variational approximation of Mather measures and sets for Tonelli Lagrangians on the flat torus, together with a numerical procedure for approximatin…
math.DS2026
Semi-discrete approximation of Mañé, Aubry and Mather sets
Fabio Camilli, Cristian Mendico
We study a variational discretization in time of Aubry--Mather theory for Tonelli Lagrangians on the flat torus. We define discrete Mañé, Aubry and Mather sets, establish their com…