ON A KIND OF SELF-SIMILAR SETS WITH COMPLETE OVERLAPS

被引：1
|
作者：
Kong, D. [1 ]
Yao, Y. [2 ]
机构：
[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China
[2] East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China
来源：
ACTA MATHEMATICA HUNGARICA | 2021年 / 163卷 / 02期
关键词：
iterated function system; self-similar set; complete overlap; spectrum; multiple coding;
D O I：
10.1007/s10474-020-01116-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let E be the self-similar set generated by the iterated function system f(0)(x) = x/beta, f1(x) = x + 1/beta, f(beta+1) = x + beta + 1/beta with beta >= 3. Then E is a self-similar set with complete overlaps, i.e., f(0) circle f(beta+ 1) = f(1) circle f(1), but E is not totally self-similar. We investigate all of its generating iterated function systems, give the spectrum of E, and determine the Hausdorff dimensions and Hausdorff measures of E and of the sets which contain all points in E having finite or infinite different codings.
引用
收藏
页码：601 / 622
页数：22
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