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On metric properties of substitutions. (English) Zbl 0696.28009
This paper considers some properties of dynamical systems \((X_{\theta},\mu_{\theta},T_{\theta})\) generated by substitutions \(\theta\) of constant length. A first result states that discrete spectrum is equivalent to rank 1, and equivalent to rigidity of \(T_{\theta}\). Among various other results we mention that the centralizer of a subclass of \(T_{\theta}'s\) is computed. This has been done with full generality by B. Host and F. Parreau [Ergodic Theory Dyn. Syst. 9, No.3, 469-477 (1989; Zbl 0662.58027)].
Reviewer: F.M.Dekking

MSC:
28D05 Measure-preserving transformations
37A99 Ergodic theory
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References:
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