WIAS Preprint No. 50, (1993)

Most β shifts have bad ergodic properties.


  • Schmeling, Jörg
    ORCID: 0000-0001-6956-9463




More than 30 years ago Rényi [1] 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 [2] 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.

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