## Equilibrium States and the Ergodic Theory of Anosov DiffeomorphismsFor 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 |

58 | |

B The Case Ф Ф | 64 |

C Attractors and Anosov Diffeomorphisms | 69 |

References | 72 |

Index | 74 |

### Other editions - View all

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms Robert Edward Bowen Limited preview - 2008 |

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms Robert Edward Bowen No preview available - 2009 |

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms R. Bowen No preview available - 2014 |

### Common terms and phrases

3-shadows a-pseudo-orbit Anosov diffeomorphism assume attractor automorphisms Axiom A diffeomorphism basic set Borel partition Borel sets Cetraro compact metric space constant continuous map cr-invariant d’Eté de Probabilités d(fnx define deﬁnition dense diam(D disjoint Dynamical Systems Ecole d’Eté Editor Émery ergodic theory function G fl G J?s Geometry Gibbs distribution Gibbs measure H^D V Hence homeomorphism hyperbolic inequality invariant measure Italy Lectures Lemma lim sup m^oo Markov partition Martina Franca Math Mathematical metric space neighborhood nonempty open cover periodic points Perron-Frobenius Theorem Picard Probabilités de Saint-Flour probability measure Proof Proposition Quantum rectangle Ruelle Rufus Bowen satisfies Axiom Sinai statistical mechanics Stochastic subset Suppose Topological entropy topologically mixing u-subrectangle unique equilibrium Variational Principle weak Bernoulli Wm(U Ws(x Wu(x Yor Eds