The link between the shape of the Aubry-Mather sets and their Lyapunov exponents

2009/02/19 by Marie-Claude Arnaud, Arnaud, Marie-Claude · 2 citations
Mathematics · Physics and Astronomy · #37C05 #37C40 #37D25 #37E40 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37C05 #msc:37C40 #msc:37D25 #msc:37E40

paper · pdf · doi:10.48550/arxiv.0902.3266

arxiv created 2009/02/19 · openalex publication_date 2009/02/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the irrational Aubry-Mather sets of an exact symplectic monotone twist map and explain what is the link between the Lyapunov exponents and the shape of such a set. The main tools that we use in the proofs are the so-called Green bundles.

Cited by

• Hyperbolicity for conservative twist maps of the 2-dimensional annulus
• Lyapunov exponents of minimizing measures for globally positive diffeomorphisms in all dimensions

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