Most β shifts have bad ergodic properties.
- Schmeling, Jörg
More than 30 years ago Rényi  introduced the representations of real numbers with an arbitrary base β > 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 β and ergodic properties of the corresponding β-shift. In this paper we will follow the bibliography of F. Blanchard  and give an affirmative answer to a question on the size of the set of real numbers β having the worst ergodic properties of their β-shifts.