Digit frequencies and Bernoulli convolutions

被引：0
|
作者：
Kempton, Tom [1 ]
机构：
[1] Univ St Andrews, Dept Math, St Andrews KY16 9SS, Fife, Scotland
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2014年 / 25卷 / 04期
基金：
英国工程与自然科学研究理事会;
关键词：
Bernoulli convolutions; Beta-expansions; Ergodic theory; MULTIFRACTAL ANALYSIS; NUMERATION; ENTROPY; REPRESENTATIONS; NUMBERS;
D O I：
10.1016/j.indag.2014.04.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is well known that when beta is a Pisot number, the corresponding Bernoulli convolution v(beta) has Hausdorff dimension less than 1, i.e. that there exists a set A(beta) with v(beta)(A(beta)) = 1 and dim(H) (A(beta)) < 1. We show explicitly how to construct for each Pisot number beta such a set A beta. (C) 2014 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V.. All rights reserved.
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页码：832 / 842
页数：11
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