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Bratteli-Vershik models for Cantor minimal systems: Applications to Toeplitz flows. (English) Zbl 0992.37008

This paper is devoted to the construction of Bratteli-Vershik models for Toeplitz flows and characterizes a class of properly ordered Bratteli diagrams corresponding to these flows. The authors’ result states that to any Choquet simpex \(K\), there exists a \(0-1\) Toeplitz flow \((Y,\psi)\), so that the set of invariant probability measures of \((Y,\psi)\) is affinely homeomorphic to \(K\) [a result of T. Downarowicz, Isr. J. Math. 74, 241-256 (1991; Zbl 0746.58047)]. They show by an explicit example, using Bratteli diagrams, that Toeplitz flows are not preserved under Kakutani equivalence, contrasting what is the case for substitution minimal systems.

MSC:

37A55 Dynamical systems and the theory of \(C^*\)-algebras
46L55 Noncommutative dynamical systems
28D20 Entropy and other invariants
54H20 Topological dynamics (MSC2010)

Citations:

Zbl 0746.58047
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