Symbolic dynamics for $\beta$-shifts and self-normal numbers
Symbolic dynamics for $\beta$-shifts and self-normal numbers
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DOI：
10.1017/s0143385797079182
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发表时间：
1997-06
影响因子：
0.9
通讯作者：
J. Schmeling
中科院分区：
文献类型：
--
作者：
J. Schmeling
30多年前，R\'enyi[1]引入了实数的任意进制表示作为$p$进制表示的推广。该领域研究最多的问题之一是基$\ β $的展开式与相应$\ β $-移位的遍历性质之间的联系。在本文中，我们将遵循Blanchard[2]的参考书目，并给出一个关于实数$\beta$具有复杂的符号动态的$\beta$-移位的集合的大小的肯定答案。
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.