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Combinatorics on Bratteli diagrams and dynamical systems. (English) Zbl 1272.37006
Berthé, Valérie (ed.) et al., Combinatorics, automata, and number theory. Cambridge: Cambridge University Press (ISBN 978-0-521-51597-9/hbk). Encyclopedia of Mathematics and its Applications 135, 324-372 (2010).
Summary: The aim of this chapter is to show how Bratteli diagrams are used to study topological dynamical systems. We illustrate their wide range of applications through classical notions: invariant measures, entropy, expansivity, representation theorems, strong orbit equivalence, eigenvalues of the Koopman operator.
For the entire collection see [Zbl 1197.68006].

MSC:
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
05C63 Infinite graphs
37A05 Dynamical aspects of measure-preserving transformations
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