## Revista Matemática Iberoamericana

### On the Conley decomposition of Mather sets

Patrick Bernard

#### Abstract

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.

#### Article information

Source
Rev. Mat. Iberoamericana, Volume 26, Number 1 (2010), 115-132.

Dates
First available in Project Euclid: 16 February 2010

https://projecteuclid.org/euclid.rmi/1266330119

Mathematical Reviews number (MathSciNet)
MR2666310

Zentralblatt MATH identifier
1193.37085

#### Citation

Bernard, Patrick. On the Conley decomposition of Mather sets. Rev. Mat. Iberoamericana 26 (2010), no. 1, 115--132. https://projecteuclid.org/euclid.rmi/1266330119

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