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.
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