Dimension Groups and Dynamical Systems

Substitutions, Bratteli Diagrams and Cantor Systems

Inbunden, Engelska, 2022

Av Fabien Durand, Dominique Perrin, Amiens) Durand, Fabien (Universite de Picardie Jules Verne

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This 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.

Produktinformation

Utgivningsdatum2022-02-03
Mått158 x 236 x 42 mm
Vikt1 039 g
FormatInbunden
SpråkEngelska
SerieCambridge Studies in Advanced Mathematics
Antal sidor760
FörlagCambridge University Press
ISBN9781108838689

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Fabien Durand is Full Professor in Mathematics at Université de Picardie Jules Verne. His interests include topological dynamical systems and the relations with theoretical computer science. He is currently the president of the Société Mathématique de France. Dominique Perrin is Emeritus Professor in Mathematics and Computer Science at Université Gustave Eiffel. He is (co)author or editor of a number of books including Profinite Semigroups and Symbolic Dynamics, Codes and Automata, Infinite Words and Combinatorics on Words (under the pseudonym Lothaire). He is a member of Academia Europea.

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.