Dimension Groups and Dynamical Systems

Fabien Durand (1) , Dominique Perrin (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including Sturmian shifts and interval exchange shifts. This is a preliminary version of a book which will be published by Cambridge University Press. Any comments are of course welcome.

Mots clés: INTERVAL EXCHANGE TRANSFORMATIONS; TOPOLOGICAL ORBIT EQUIVALENCE; RAUZY INDUCTION; GEOMETRIC REPRESENTATION; MINIMAL HOMEOMORPHISMS; LINEAR REPETITIVITY; UNIQUE ERGODICITY; VERSHIK MODELS; MARKOV-CHAINS; RETURN WORDS

Domaines: Systèmes dynamiques [math.DS]

Fabien Durand, Dominique Perrin. Dimension Groups and Dynamical Systems: Substitutions, Bratteli Diagrams and Cantor Systems. Cambridge University Press, 196, 2022, Cambridge Studies in Advanced Mathematics, ⟨10.1017/9781108976039⟩. ⟨hal-03746074⟩