On Aubry sets and Mather's action functional
Dynamical Systems
2007-05-23 v3
Abstract
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.
Cite
@article{arxiv.math/0102147,
title = {On Aubry sets and Mather's action functional},
author = {Daniel Massart},
journal= {arXiv preprint arXiv:math/0102147},
year = {2007}
}
Comments
17 pages, 2nd version