On Aubry sets and Mather's action functional

Details On Aubry sets and Mather's action functional On Aubry sets and Mather's action functional

2001-02-19

arxiv.org/abs/math/0102147v3

Israel J. Math. 134 (2003), 157--171

Mathematics

Dynamical Systems

17 pages, 2nd version

Scientific paper

We study Lagrangian systems on a closed manifold. We link the differentiability of Mather's beta-function with the topological complexity of the complement of the Aubry set. As a consequence, when the dimension of the manifold is less than or equal to two, the differentiability of the beta-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 a conjecture by Ricardo Mane.

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