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The centralizer of Morse shifts. (English) Zbl 0587.28016
We examine the centralizer of Morse shifts. 1. Let \(x=b^ 0\times b^ 1\times...\) be a regular Morse sequence and \(| b^ i| \leq r.\) Then \(a)\quad C(T)=\{T^ i\sigma^ j: i\in Z,\quad j=0,1\},\) where C(T) means the centralizer of T, T is the shift, and \(\sigma\) is the mirror map. b) There are no roots of T. 2. There are Morse shifts with uncountable centralizer. Let \({\mathcal T}^{\{n_ t\}}\) be the class of all ergodic automorphisms \(\tau\) with \(\exp (2\pi i/n_ t)\) in the point spectrum of \(\tau\). We introduce some number \(d^{\{n_ t\}}(\tau)\) for \(\tau \in {\mathcal T}^{\{n_ t\}}\) and prove that if \(d^{\{n_ t\}}(\tau)<\infty\) then \(\tau\) is coalescent.

MSC:
28D10 One-parameter continuous families of measure-preserving transformations
37A99 Ergodic theory
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