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Toeplitz flows, ordered Bratteli diagrams and strong orbit equivalence

Published online by Cambridge University Press:  28 November 2001

FUMIAKI SUGISAKI
FUMIAKI SUGISAKI
Affiliation:
Department of Mathematics, Keio University, 3-14-1 Hiyoshi Kohoku-ku, Yokohama 223-8522, Japan (e-mail: [email protected]) Faculty of Science, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan (e-mail: [email protected])
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Abstract

Let (X,T) be a Cantor minimal system associated with a properly ordered Bratteli diagram with the equal path number property. In this paper we will show that there exists a Toeplitz flow (Y,S) such that (X,T) and (Y,S) are strongly orbit equivalent. This is an affirmative answer to the open problem in R. Gjerde and Ø. Johansen (Bratteli–Vershik models for Cantor minimal systems: applications to Toeplitz flows. Ergod. Th. & Dynam. Sys.20 (2000), 1687–1710).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 6 , December 2001 , pp. 1867 - 1881
Copyright
2001 Cambridge University Press

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