Hausdorff dimension of certain sets arising in Engel expansions

被引：14

作者：

Fang, Lulu ^{[1
]}

Wu, Min ^{[2
]}

机构：

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China

[2] South China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China

来源：

NONLINEARITY | 2018年 / 31卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Engel expansions; growth rate of digits; Hausdorff dimension; MODERATE DEVIATION PRINCIPLES; CONTINUED FRACTIONS; PARTIAL QUOTIENTS; EXCEPTIONAL SETS; OPPENHEIM SERIES; SEQUENCES; GROWTH;

D O I：

10.1088/1361-6544/aaaaf9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present paper is concerned with the Hausdorff dimension of certain sets arising in Engel expansions. In particular, the Hausdorff dimension of the set {x is an element of (0, 1) : A(n)(x) >= phi(n) for infinitely many n} is completely determined, where A(n)(x) can stand for the digit, gap and ratio between two consecutive digits in the Engel expansion of x and phi is a positive function defined on natural numbers. These results significantly extend the existing results of Galambos' open problems on the Hausdorff dimension of sets related to the growth rate of digits.

引用

页码：2105 / 2125

页数：21

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