SYMBOLIC DYNAMICS FOR BETA-SHIFTS AND SELF-NORMAL NUMBERS

More than 30 years ago Renyi [1] introduced the representations of rea l 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 bibliog raphy 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.