Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

• Main Author: Bowen, Rufus (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Chazottes, Jean-René (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Lecture Notes in Mathematics, 470
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Probabilities.; Manifolds (Mathematics).; Complex manifolds.; Dynamical Systems and Ergodic Theory.; Manifolds and Cell Complexes (incl. Diff.Topology).; Probability Theory and Stochastic Processes.

For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new a...

Table of Contents:

• Preface to the 2nd edition by David Ruelle
• 0. Introduction
• 1.Gibbs measures
• A.Gibbs measures
• B.Ruelle's Perron-Frobenius Theorem
• C.Construction of Gibbs measures
• D.Variational principle
• E.Further properties
• References
• 2.General thermodynamic formalism
• A.Entropy
• B.Pressure
• C.Variational principle
• D.Equilibrium states
• References
• 3.Axiom A diffeomorphisms
• A.Definition
• B. Spectral decomposition
• C.Markov partitions
• D.Symbolic dynamics
• References
• 4.Ergodic theory of Axiom A diffeomorphisms
• A.Equilibrium states for basic sets
• B.The case phi=phi^(u)
• C.Attractors and Anosov diffeormorphisms
• References
• Index.