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This book is the first self-contained exposition of the link between dynamical systems and dimension groups. Recommended for graduate students as well as established researchers, it contains a thorough introduction to the field, including full proofs of the major results, as well a wealth of examples, exercises and open problems.
List 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.
About the author
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.
Summary
This book is the first self-contained exposition of the link between dynamical systems and dimension groups. Recommended for graduate students as well as established researchers, it contains a thorough introduction to the field, including full proofs of the major results, as well a wealth of examples, exercises and open problems.
