Revista Matemática Iberoamericana

On the Conley decomposition of Mather sets

Patrick Bernard

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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

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

First available in Project Euclid: 16 February 2010

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Zentralblatt MATH identifier

Primary: 37J50: Action-minimizing orbits and measures 37B20: Notions of recurrence 49L25: Viscosity solutions

semi-continuity of the Aubry set minimizing measures chain transitivity


Bernard, Patrick. On the Conley decomposition of Mather sets. Rev. Mat. Iberoamericana 26 (2010), no. 1, 115--132.

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