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Substitutions, adic transformations, and beta-expansions. (English) Zbl 0771.28013
Symbolic dynamics and its applications, Proc. AMS Conf. in honor of R. L. Adler, New Haven/CT (USA) 1991, Contemp. Math. 135, 361-372 (1992).
Summary: [For the entire collection see Zbl 0755.00019.]
It is shown that dynamical systems corresponding to a class of substitutions of nonconstant length have purely discrete spectrum. The proof relies on properties of digit expansions with non-integral bases.

MSC:
28D05 Measure-preserving transformations
37A30 Ergodic theorems, spectral theory, Markov operators
11A67 Other number representations
68Q45 Formal languages and automata
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