Ergodic

This book treats mainly some basic topics of ergodic theory in a revised form, bringing into focus its interactions with classical descriptive set theory more than is normally the practice. The presentation has a slow pace and can be read by anyone with a background in measure theory and point set topology. In particular, the first two chapters, the core of ergodic theory, can form a course of four to six lectures at third year B.Sc., M.Sc., or M.Phil. level in Indian Uni- versities. I have borrowed freely from existing texts ( with acknowledgements) but the overall theme of the book falls in the complement of these.

Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations.

This book focuses on the interpretation of ergodic optimal problems as questions of variational dynamics, employing a comparable approach to that of the Aubry-Mather theory for Lagrangian systems.

Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics.

This book summarizes and highlights progress in our understanding of Dy­ namical Systems during six years of the German Priority Research Program "Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems" .