Aubry–Mather theory on graphs

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Abstract

We formulate Aubry–Mather theory for Hamiltonians/Lagrangians defined on graphs, study the structure of minimizing measures, and discuss the relationship with weak KAM theory developed in Siconolfi and Sorrentino (2018 Anal. PDE 1 171–211). Moreover, we describe how to transport and interpret these results on networks.