Overview
- Provides a full account of the problem of finite invariant measures for measurable transformations with a detailed explanation of its history
- Explains in detail the properties and significance of weakly wandering and other sequences of integers attached to infinite ergodic transformations
- Shows interesting new connections between ergodic theory and certain number theoretic problems
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (7 chapters)
Keywords
About this book
The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure.
This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader.
Reviews
“This is a well-written book that should be the place to go to for someone interested in weakly wandering sequences, their properties and extensions. Most of the work the authors discuss is the result of their research over a number of years. At the same time we would have liked to see discussions of several topics that are connected to the topics of the book, such as inducing, rank-one transformations, and Maharam transformations.” (Cesar E. Silva, Mathematical Reviews, May, 2016)
“The subject of the book under review is ergodic theory with a stress on WW sequences. … The book is interesting, well written and contains a lot of examples. It constitutes a valuable addition to the mathematical pedagogical literature.” (Athanase Papadopoulos, zbMATH, 1328.37006, 2016)
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Weakly Wandering Sequences in Ergodic Theory
Authors: Stanley Eigen, Arshag Hajian, Yuji Ito, Vidhu Prasad
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-4-431-55108-9
Publisher: Springer Tokyo
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Japan 2014
Hardcover ISBN: 978-4-431-55107-2Published: 01 September 2014
Softcover ISBN: 978-4-431-56400-3Published: 23 August 2016
eBook ISBN: 978-4-431-55108-9Published: 19 August 2014
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XIV, 153
Number of Illustrations: 15 b/w illustrations
Topics: Dynamical Systems and Ergodic Theory, Number Theory, Measure and Integration, Functional Analysis