Aubry-Mather theory on graphs
Antonio Siconolfi, Alfonso Sorrentino
TL;DR
This paper extends Aubry-Mather theory to Hamiltonians and Lagrangians on graphs, exploring its connection with weak KAM theory to deepen understanding of dynamical systems on discrete structures.
Contribution
It introduces a novel formulation of Aubry-Mather theory specifically for graph-based Hamiltonian and Lagrangian systems, linking it with weak KAM theory.
Findings
Aubry-Mather theory adapted to graphs.
Relationship established between Aubry-Mather and weak KAM theories on graphs.
Potential applications in discrete dynamical systems.
Abstract
We formulate Aubry-Mather theory for Hamiltonians/Lagrangians defined on graphs and discuss its relationship with weak KAM theory developed in [24].
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology