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.
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.
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.
Inhaltsangabe
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.
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.
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