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Substitutional dynamical systems, Bratteli diagrams and dimension groups

Published online by Cambridge University Press:  02 April 2001

F. DURAND ,
B. HOST  and
C. SKAU
F. DURAND
Affiliation:
Université de Picardie Jules Verne, Faculté de Mathématiques et Imformatique, 33, Rue Saint-Leu, F 80 039 Armiens Cédex 01, France
B. HOST
Affiliation:
Université de Marne la Vallée, 2 rue de la Butte verte, F 93 166 Noisy le Grand Cedex, France
C. SKAU
Affiliation:
Department of Mathematics and Statistics, NTNU, 7055 Dragvoll, Norway
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Abstract

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We explore 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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 4 , August 1999 , pp. 953 - 993
Copyright
1999 Cambridge University Press