More than 30 years ago R\'enyi  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  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.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
* Views captured on Cambridge Core between September 2016 - 25th May 2017. This data will be updated every 24 hours.