Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

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Springer Science & Business Media, Apr 17, 2008 - Mathematics - 73 pages
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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 at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."

 

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Contents

Gibbs Measures
3
B Ruelles PerronFrobenius Theorem
8
C Construction of Gibbs Measures
13
D Variational Principle
16
E Further Properties
22
References
26
B Pressure
32
C Variational Principle
36
B Spectral Decomposition
47
C Markov Partitions
51
D Symbolic Dynamics
56
References
58
B The Case Ф Ф
64
C Attractors and Anosov Diffeomorphisms
69
References
72
Index
74

D Equilibrium States
42
References
43

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