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On the Conley decomposition of Mather sets
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version 2 october2008 |
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Authors: Patrick Bernard.
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| Revista Matematica Iberoamericana 26, No. 1 (2010), 115-132. | ||
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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. |
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Résumé: Dans le contexte de la théorie de Mather des systèmes Lagrangiens, on étudie la décomposition en composantes transitives par chaines des ensembles invariants de Mather. Comme application, on montre, sous des hypothèses appropriées, la semi-continuité de l'ensemble d'Aubry. |