On Aubry Sets and Mather ’ S Action Functional 2

@inproceedings{Massart2001OnAS,
  title={On Aubry Sets and Mather ’ S Action Functional 2},
  author={Daniel Massart},
  year={2001}
}
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. 

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