Maximizing Bernoulli measures and dimension gaps for countable branched systems
Maximizing Bernoulli measures and dimension gaps for countable branched systems
复制标题
DOI：
10.1017/etds.2020.41
复制
发表时间：
2018-02
影响因子：
0.9
通讯作者：
S. Baker;Natalia Jurga
中科院分区：
文献类型：
--
作者：
S. Baker;Natalia Jurga
Kifer，Peres和韦斯在[A]中证明了具有独立数字的连续分数的维数间隙。Israel J. Math. 124（2001），61-76]证明了存在$c_{0}>0$，使得对于任意概率测度$\unicode[STIX]{x1 D 707}$，$\dim \unicode[STIX]{x1 D 707}\leq 1-c_{0}$，使得连分式展开式的位独立同分布。本文证明了在这类测度中，存在一个维数最大的测度。我们的结果也适用于更一般的设置可数分支系统。
Kifer, Peres, and Weiss proved in [A dimension gap for continued fractions with independent digits. Israel J. Math. 124 (2001), 61–76] that there exists $c_{0}>0$ , such that $\dim \unicode[STIX]{x1D707}\leq 1-c_{0}$ for any probability measure $\unicode[STIX]{x1D707}$ , which makes the digits of the continued fraction expansion independent and identically distributed random variables. In this paper we prove that amongst this class of measures, there exists one whose dimension is maximal. Our results also apply in the more general setting of countable branched systems.