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

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

Dimension Groups and Dynamical Systems

Substitutions, Bratteli Diagrams and Cantor Systems

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

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English

Cambridge University Press
03 February 2022

Algebra; Groups & group theory; Calculus & mathematical analysis; Topology; Dynamics & statics

Series: Cambridge Studies in Advanced Mathematics

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.

By: Fabien Durand (Universite de Picardie Jules Verne Amiens), Dominique Perrin
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: New edition
Dimensions: Height: 236mm, Width: 158mm, Spine: 42mm
Weight: 1.039kg
ISBN: 9781108838689
ISBN 10: 1108838685
Series: Cambridge Studies in Advanced Mathematics
Pages: 760
Publication Date: 03 February 2022
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

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.

Fabien Durand is Full Professor in Mathematics at Universite de Picardie Jules Verne. His interests include topological dynamical systems and the relations with theoretical computer science. He is currently the president of the Societe Mathematique de France. Dominique Perrin is Emeritus Professor in Mathematics and Computer Science at Universite 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.