Hostname: page-component-7c8c6479df-7qhmt Total loading time: 0 Render date: 2024-03-28T10:59:23.950Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  01 June 1997

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

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
Copyright
1997 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)