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The rank of regular Morse dynamical systems. (English) Zbl 0549.28026
If \(x=b\cdot^{0}\times b\cdot^{1}\times..\). is a regular Morse sequence and \(\sup| b^ i| <+\infty\), then x has rank 2. There are regular Morse shifts with rank one. If x is a Kakutani sequence, then x has rank one iff x is not regular. If \(\Theta\) is a nonperiodic substitution of constant length on two symbols, then \(\Theta\) is of rank 2 iff \(\Theta\) is a continuous substitution. Every Morse sequence has a simple spectrum.

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