Bowen R. Equilibrium states and the ergodic theory of Anosov diffeomorphisms / ed. by Chazottes J-R.; Preface by Ruelle D. - 2nd rev. - Berlin; Heidelberg: Springer, 2008. - viii, 73 p.: ill. - (Lecture notes in mathematics; 470). - Incl. bibl. ref. and index. - ISBN 978-3-540-77605-5  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

0 Introduction ................................................. 1 1. Gibbs Measures .............................................. 3 A. Gibbs Distribution ....................................... 3 B. Ruelle's Perron-Frobenius Theorem ........................ 8 C. Construction of Gibbs Measures .......................... 13 D. Variational Principle ................................... 16 E. Further Properties ...................................... 22 References ................................................. 26 2. General Thermodynamic Formalism ............................ 29 A. Entropy ................................................. 29 B. Pressure ................................................ 32 C. Variational Principle ................................... 36 D. Equilibrium States ...................................... 42 References ................................................. 43 3. Axiom a Diffeomorphisms .................................... 45 A. Definition .............................................. 45 B. Spectral Decomposition .................................. 47 C. Markov Partitions ....................................... 51 D. Symbolic Dynamics ....................................... 56 References ................................................. 58 4. Ergodic Theory of Axiom a Diffeomorphisms .................. 61 A. Equilibrium States for Basic Sets ....................... 61 B. The Case Ø = Ø(u) ........................................ 64 C. Attractors and Anosov Diffeomorphisms ................... 69 References ................................................. 72 Index ......................................................... 75