Infinite Ergodic Theory of Numbers

By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples.

Contents:

Preface

Mathematical symbols

Number-theoretical dynamical systems

Basic ergodic theory

Renewal theory and α-sum-level sets

Infinite ergodic theory

Applications of infinite ergodic theory

Bibliography

Index