Journal
NONLINEARITY
Volume 36, Issue 11, Pages 5819-5859Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-6544/acf6ef
Keywords
Aubry-Mather theory; Hamiltonians on networks; weak KAM
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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.
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.
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