Dimension Groups and Dynamical Systems: Substitutions, Bratteli Diagrams and Cantor Systems

ISBN-13: 9781108838689 / Angielski / Twarda / 2022 / 760 str.

Dominique Perrin

Opis

This is the first self-contained exposition of the connections between symbolic dynamical systems, dimension groups and Bratteli diagrams.

Recenzje

'… 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

Spis treści

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.