Local product structure for Equilibrium States

1999/11/17 by Renaud Leplaideur · 44 citations
Mathematics · #Algorithm #Axiom #Diffeomorphism #Geometry #Manifold (fluid mechanics) #Mathematical Dynamics and Fractals #Mathematical economics #Mathematics #Product (mathematics) #Pure mathematics #State (computer science) #Thermodynamic equilibrium #sort

paper · pdf · doi:10.1090/s0002-9947-99-02479-4

published in Transactions of the American Mathematical Society 352(4), 1889-1912 (American Mathematical Society)

openalex publication_date 1999/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The usual way to study the local structure of Equilibrium State of an Axiom-A diffeomorphism or flow is to use the symbolic dynamic and to push results on the manifold. A new geometrical method is given. It consists in proving that Equilibrium States for Hölder-continuous functions are related to other Equilibrium States of some special sub-systems satisfying a sort of expansiveness. Using different kinds of extensions the local product structure of Gibbs-measure is proven.

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• Rigidity of measures on the torus: smooth stabilizers and entropy
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• Chaos : Butterflies also generate phase transitions and parallel universes
• Characterizing Symmetric Spaces by their Lyapunov Spectra
• Central limit theorem for dimension of Gibbs measures for skew expanding maps
• Large deviation for return times in open sets for axiom A diffeomorphisms
• Birkhoff averages of Poincare cycles for Axiom-A diffeomorphisms
• The space of Anosov diffeomorphisms

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