On Aubry sets and Mather’s action functional

By D. Massart. 2001

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We study Lagrangian systems on a closed manifoldM. We link the differentiability of Mather’sβ-function with the topological complexity of the complement of the Aubry set. As a consequence, whenM is a closed, orientable surface, the differentiability of theβ-function at a given homology class is forced by the irrationality of the homology class. This allows us to prove the two-dimensional case of a conjecture by Mañé.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9efd5c719de64c0f789aeb93f64db36f475a10e1