On the Conley decomposition of Mather sets

Patrick Bernard (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: chain transitivity; semi-continuity of the Aubry set; minimizing measures; chain transitivity.

Domaines: Systèmes dynamiques [math.DS]

Patrick Bernard. On the Conley decomposition of Mather sets. Revista Matemática Iberoamericana, 2010, 26 (1), pp.115-132. ⟨hal-00294640v2⟩