Dimension groups and dynamical systems: substitutions, Bratteli diagrams and cantor systems
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,...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge ; New York, NY
Cambridge University Press
2022
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| Series: | Cambridge studies in advanced mathematics
196 |
| Subjects: | |
| Links: | https://doi.org/10.1017/9781108976039 https://doi.org/10.1017/9781108976039 https://doi.org/10.1017/9781108976039 |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 24 Jan 2022) Topological dynamical systems -- Ordered groups -- Ordered cohomology groups -- Partitions in towers -- Bratteli diagrams -- Substitution shifts and generalizations -- Dendric shifts -- Interval exchange transformations -- Bratteli diagrams and C*-algebras |
| Physical Description: | 1 Online-Ressource (vii, 584 Seiten) |
| ISBN: | 9781108976039 |
| DOI: | 10.1017/9781108976039 |
Staff View
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| 520 | |a 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 | ||
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| id | DE-604.BV047847769 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T19:30:04Z |
| institution | BVB |
| isbn | 9781108976039 |
| language | English |
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| physical | 1 Online-Ressource (vii, 584 Seiten) |
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| publishDate | 2022 |
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| publisher | Cambridge University Press |
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| series2 | Cambridge studies in advanced mathematics 196 |
| spelling | Durand, Fabien 1969- (DE-588)1021290203 aut Dimension groups and dynamical systems substitutions, Bratteli diagrams and cantor systems Fabien Durand, Dominique Perrin Cambridge ; New York, NY Cambridge University Press 2022 1 Online-Ressource (vii, 584 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 196 Title from publisher's bibliographic system (viewed on 24 Jan 2022) Topological dynamical systems -- Ordered groups -- Ordered cohomology groups -- Partitions in towers -- Bratteli diagrams -- Substitution shifts and generalizations -- Dendric shifts -- Interval exchange transformations -- Bratteli diagrams and C*-algebras 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 Dynamics Group theory Dimension theory (Topology) Perrin, Dominique 1946- (DE-588)129256250 aut Erscheint auch als Druck-Ausgabe 978-1-108-83868-9 https://doi.org/10.1017/9781108976039 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Durand, Fabien 1969- Perrin, Dominique 1946- Dimension groups and dynamical systems substitutions, Bratteli diagrams and cantor systems Dynamics Group theory Dimension theory (Topology) |
| title | Dimension groups and dynamical systems substitutions, Bratteli diagrams and cantor systems |
| title_auth | Dimension groups and dynamical systems substitutions, Bratteli diagrams and cantor systems |
| title_exact_search | Dimension groups and dynamical systems substitutions, Bratteli diagrams and cantor systems |
| title_full | Dimension groups and dynamical systems substitutions, Bratteli diagrams and cantor systems Fabien Durand, Dominique Perrin |
| title_fullStr | Dimension groups and dynamical systems substitutions, Bratteli diagrams and cantor systems Fabien Durand, Dominique Perrin |
| title_full_unstemmed | Dimension groups and dynamical systems substitutions, Bratteli diagrams and cantor systems Fabien Durand, Dominique Perrin |
| title_short | Dimension groups and dynamical systems |
| title_sort | dimension groups and dynamical systems substitutions bratteli diagrams and cantor systems |
| title_sub | substitutions, Bratteli diagrams and cantor systems |
| topic | Dynamics Group theory Dimension theory (Topology) |
| topic_facet | Dynamics Group theory Dimension theory (Topology) |
| url | https://doi.org/10.1017/9781108976039 |
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