Dimension groups and dynamical systems : substitutions, Bratteli diagrams and cantor systems / Fabien Durand, Dominique Perrin.

Format:

Book

Author/Creator:

Durand, Fabien, 1969- author.

Perrin, Dominique, author.

Series:

Cambridge studies in advanced mathematics ; 196.

Cambridge studies in advanced mathematics ; 196

Language:

English

Subjects (All):

Dynamics.

Group theory.

Dimension theory (Topology).

Physical Description:

1 online resource (vii, 584 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2022.

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 24 Jan 2022).

ISBN:

1-108-98609-9

1-108-97603-4

OCLC:

1306060568