RESONANCE BETWEEN SELF-SIMILAR SETS AND THEIR UNIVOQUE SETS

被引：1

作者：

Chen, Chen ^{[1
]}

Ma, Ying ^{[1
]}

Lei, Lei ^{[1
]}

Gareeb, Mohammad ^{[2
]}

Jiang, Kan ^{[1
]}

机构：

[1] Ningbo Univ, Dept Math, Ningbo, Peoples R China

[2] East China Normal Univ, Dept Math, Beijing, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2021年 / 29卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Bi-Lipschitz Equivalence; Self-Similar Set; Univoque Set; LIPSCHITZ EQUIVALENCE; HAUSDORFF DIMENSION; REAL NUMBERS; EXPANSIONS;

D O I：

10.1142/S0218348X21501115

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a self-similar set in Double-struck capital R. Generally, if the iterated function system (IFS) of K has some overlaps, then some points in K may have multiple codings. If an x is an element of K has a unique coding, then we call x a univoque point. We denote by U (univoque set) the set of points in K having unique codings. In this paper, we shall consider the following natural question: if two self-similar sets are bi-Lipschitz equivalent, then are their associated univoque sets also bi-Lipschitz equivalent. We give a class of self-similar sets with overlaps, and answer the above question affirmatively.

引用

页数：12

共 26 条

[1] ENTROPY, TOPOLOGICAL TRANSITIVITY, AND DIMENSIONAL PROPERTIES OF UNIQUE q-EXPANSIONS [J].