On Aubry Sets and Mather’s Action Functional

Abstract

We study Lagrangian systems on a closed manifold M . We link the differentiability of Mather’s β -function with the topological complexity of the complement of the Aubry set. As a consequence, when dimM ≤ 3, the differentiability of the β -function at a given homology class is forced by the irrationality of the homology class. As an application we prove the two-dimensional case of two conjectures by Mañé.

Cite this paper

@inproceedings{Massart2001OnAS, title={On Aubry Sets and Mather’s Action Functional}, author={Daniel Massart}, year={2001} }