In the context of Mather’s theory of Lagrangian systems, we study the decomposition in chain-transitive classes of the Mather invariant sets. As an application, we prove, under appropriate hypotheses, the semi-continuity of the so-called Aubry set as a function of the Lagrangian.
Cite this article
Patrick Bernard, On the Conley decomposition of Mather sets. Rev. Mat. Iberoam. 26 (2010), no. 1, pp. 115–132