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Finite-rank Bratteli–Vershik diagrams are expansive

Published online by Cambridge University Press:  01 June 2008

Institute of Mathematics, Technical University, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland (email:
Department of Mathematical Engineering and Center of Mathematical Modeling, University of Chile, Av. Blanco Encalada 2120, 5to piso, Santiago, Chile (email:


The representation of Cantor minimal systems by Bratteli–Vershik diagrams has been extensively used to study particular aspects of their dynamics. A main role has been played by the symbolic factors induced by the way vertices of a fixed level of the diagram are visited by the dynamics. The main result of this paper states that Cantor minimal systems that can be represented by Bratteli–Vershik diagrams with a uniformly bounded number of vertices at each level (called finite-rank systems) are either expansive or topologically conjugate to an odometer. More precisely, when expansive, they are topologically conjugate to one of their symbolic factors.

Research Article
Copyright © Cambridge University Press 2008

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