On the Conley decomposition of Mather sets
Patrick Bernard (CEREMADE)
TL;DR
This paper investigates the decomposition of Mather invariant sets into chain-transitive classes within Lagrangian systems and proves semi-continuity of the Aubry set as a function of the Lagrangian under certain conditions.
Contribution
It introduces a detailed analysis of the Conley decomposition of Mather sets and establishes semi-continuity results for the Aubry set in this context.
Findings
Decomposition of Mather sets into chain-transitive classes.
Semi-continuity of the Aubry set as a function of the Lagrangian.
Application of the decomposition to Lagrangian dynamics.
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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Taxonomy
TopicsQuantum chaos and dynamical systems · Geometric and Algebraic Topology · Mathematical Dynamics and Fractals