Infinite Ergodic Theory of Numbers (De Gruyter Textbook)

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 * A unique coverage of the relation between infinite ergodic theory and number theory. * Example solutions to select exercises included in the appendix. * Useful for a course serving master (and advanced bachelor) and PhD students. 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 By connecting dynamical systems and number theory this graduate textbook on ergodic theory covers a highly active area of mathematics, where a variety of strands of research open up. After introducing number-theoretical dynamical systems, the text touches on foundations and renewal theory before covering infinite ergodic theory. Applications such as continued fraction expansion and sum-level sets are discussed as well.