Substitutional dynamical systems, Bratteli diagrams and dimension groups

Fabien Durand (1) , Bernard Host (2) , Christian Skau

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit, and render an effective method to compute an invariant of (ordered) $K$-theoretic nature for these systems. This new invariant is independent of spectral invariants which have previously been extensively studied. Before we state the main results we give some background.

Mots clés: dimension groups; substitutions; linearly recurrent

Domaines: Systèmes dynamiques [math.DS]

Fabien Durand, Bernard Host, Christian Skau. Substitutional dynamical systems, Bratteli diagrams and dimension groups. Ergodic Theory and Dynamical Systems, 1999, 19, pp.953-993. ⟨hal-00304369⟩