Aubry-Mather theory on graphs

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.

Automated summary

We present the Aubry-Mather theory for Hamiltonians/Lagrangians defined on graphs, analyze the structure of minimizing measures, and explore their connection with the weak KAM theory developed by Siconolfi and Sorrentino (2018 Anal. PDE 1 171-211). Additionally, we demonstrate how these results can be transported and interpreted in the context of networks.