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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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##### References:
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