Equilibrium States in Ergodic Theory [Paperback]

Based on a one semester course, this book provides a self contained introduction to the ergodic theory of equilibrium states.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.The text is self contained except for some measure theoretic prerequisites which are listed (with references to the literature) in an appendix.Unlike most other books on ergodic theory the text emphasises applications of the general theory to important specific examples like the Ising model, interval maps and iterated function systems.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.The text is self contained except for some measure theoretic prerequisites which are listed (with references to the literature) in an appendix.Unlike most other books on ergodic theory the text emphasises applications of the general theory to important specific examples like the Ising model, interval maps and iterated function systems.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 that 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-Ruls±