Skip to content
Register Sign in Wishlist

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


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: February 2022
  • availability: Available
  • format: Hardback
  • isbn: 9781108838689

£ 64.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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.

    • The first self-contained, systematic account of the topic
    • Contains nearly 250 exercises with solutions provided
    • Features a list of open problems to encourage new directions of research
    Read more

    Reviews & endorsements

    'This substantial monograph comprises the first thorough and self-contained exposition of the theory of dimension groups in topological dynamics … It is a welcome addition to the dynamics literature in an area of much activity with links to several other disciplines, including operator algebras and computer science.' Thomas B. Ward, zbMATH

    '… an impressive self-contained expository presentation that explores the connections between properties of topological dynamical systems and their dimension groups. The book is a rich source of material on topological and symbolic dynamics and will be useful for both graduate students in mathematics or computer science and experienced researchers.' Olena Karpel, MathSciNet

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: February 2022
    • format: Hardback
    • isbn: 9781108838689
    • length: 760 pages
    • dimensions: 236 x 158 x 42 mm
    • weight: 1.039kg
    • availability: Available
  • Table of Contents

    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
    Name index
    Index of symbols
    Subject index.

  • Authors

    Fabien Durand, Université de Picardie Jules Verne, Amiens
    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, Université Gustave Eiffel, 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.

Related Books

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.