Aubry-mather Theory for Multi-dimensional Maps
نویسنده
چکیده
In this paper we study a discrete multi-dimensional version of Aubry-Mather theory. We set this problem as an infinite dimensional linear programming problem and study its relations to Monge-Kantorowich optimal transport. The dual problem turns out to be a discrete analog of the Hamilton-Jacobi equations. As in optimal transport, Monge-Ampére equations also play a role in this problem. We present some applications to discretizations of Lagrangian systems.
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تاریخ انتشار 2002