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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
Sara Munday, University of Bologna, Italy;
Marc Kesseböhmer and Bernd Stratmann, University of Bremen, Germany.