Equilibrium States in Ergodic Theory

Based on a one semester course, this book provides a self contained introduction to the ergodic theory of equilibrium states.

Gerhard Keller (Author)

9780521595346, Cambridge University Press

Paperback, published 22 January 1998

192 pages, 20 b/w illus.
22.7 x 15.3 x 1.1 cm, 0.29 kg

'This is a very well-written book. It is well organised, clear, and coherent … It would also be suitable as a basis for a very good graduate course.' Hans Crauel, Bulletin of the London Mathematical Society

This book provides a detailed introduction to the ergodic theory of equilibrium states giving equal weight to two of its most important applications, namely to equilibrium statistical mechanics on lattices and to (time discrete) dynamical systems. It starts with a chapter on equilibrium states on finite probability spaces which introduces the main examples for the theory on an elementary level. After two chapters on abstract ergodic theory and entropy, equilibrium states and variational principles on compact metric spaces are introduced emphasizing their convex geometric interpretation. Stationary Gibbs measures, large deviations, the Ising model with external field, Markov measures, Sinai-Bowen-Ruelle measures for interval maps and dimension maximal measures for iterated function systems are the topics to which the general theory is applied in the last part of the book. The text is self contained except for some measure theoretic prerequisites which are listed (with references to the literature) in an appendix.

1. Simple examples of equilibrium states
2. Some basic ergodic theory
3. Entropy
4. Equilibrium states and pressure
5. Gibbs measures
6. Equilibrium states and derivatives
Appendix: Background material.

Subject Areas: Calculus & mathematical analysis [PBK]