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Symbolic dynamics for $\beta$-shifts and self-normalnumbers

Published online by Cambridge University Press:  01 June 1997

JÖRG SCHMELING
JÖRG SCHMELING
Affiliation:
Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany
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Abstract

More than 30 years ago R\'enyi [1] introduced the representations of real numbers with an arbitrary base $\beta > 1$ as a generalization of the $p$-adic representations. One of the most studied problems in this field is the link between expansions to base $\beta$ and ergodic properties of the corresponding $\beta$-shift.

In this paper we will follow the bibliography of Blanchard [2] and give an affirmative answer to a question on the size of the set of real numbers $\beta$ having complicated symbolic dynamics of their $\beta$-shifts.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 3 , June 1997 , pp. 675 - 694
Copyright
1997 Cambridge University Press

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