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.

‘This is an excellent book for a one-semester course in ergodic theory … The overall presentation of the material is very appealing as it avoids pedantry and includes a variety of examples and exercises.’

N. T. A. Haydn Source: ZAMM

‘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 Source: Bulletin of the London Mathematical Society