Dimension Groups and Dynamical Systems
Dimension Groups and Dynamical Systems
Dominique Perrin, Université Gustave Eiffel, France
$84.99
USDThis book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition – with full proofs – of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.
- The first self-contained, systematic account of the topic
- Contains nearly 250 exercises with solutions provided
- Features a list of open problems to encourage new directions of research
Reviews & endorsements
‘This substantial monograph comprises the first thorough and self-contained exposition of the theory of dimension groups in topological dynamics … It is a welcome addition to the dynamics literature in an area of much activity with links to several other disciplines, including operator algebras and computer science.’ Thomas B. Ward, zbMATH
‘… an impressive self-contained expository presentation that explores the connections between properties of topological dynamical systems and their dimension groups. The book is a rich source of material on topological and symbolic dynamics and will be useful for both graduate students in mathematics or computer science and experienced researchers.’ Olena Karpel, MathSciNet
‘A valuable resource, especially for those interested in the dimension groups and Vershik maps as related to low complexity subshifts.’ Mike Boyle, Bulletin of the American Mathematical Society
Product details
January 2022Adobe eBook Reader
9781108986090
0 pages
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Introduction
- 1. Topological dynamical systems
- 2. Ordered groups
- 3. Ordered cohomology groups
- 4. Partitions in towers
- 5. Bratteli diagrams
- 6. Substitution shifts and generalizations
- 7. Dendric shifts
- 8. Interval exchange transformations
- 9. Bratteli diagrams and C*-algebras
- Appendix A. Solutions to exercises
- Appendix B. Useful definitions and results
- Appendix C. Summary of examples
- Appendix D. Equivalent definitions of Sturmian shifts
- Appendix E. Open problems
- References
- Name index
- Index of symbols
- Subject index.
