Revista Matemática Iberoamericana

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Volume 26, Issue 1, 2010, pp. 115–132
DOI: 10.4171/RMI/596

Published online: 2010-04-30

On the Conley decomposition of Mather sets

Patrick Bernard[1]

(1) Université de Paris Dauphine, France

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.

Keywords: Semi-continuity of the Aubry set, minimizing measures, chain transitivity

Bernard Patrick: On the Conley decomposition of Mather sets. Rev. Mat. Iberoamericana 26 (2010), 115-132. doi: 10.4171/RMI/596