Lipschitz equivalence of a class of general Sierpinski carpets

被引：18

作者：

Wen, Zhixiong ^{[2
]}

Zhu, Zhiyong ^{[1
]}

Deng, Guotai ^{[3
]}

机构：

[1] NW A&F Univ, Coll Sci, Yangling 712100, Shanxi, Peoples R China

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[3] Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 385卷 / 01期

关键词：

Fractal; Lipschitz equivalence; General Sierpinski carpet; Self-similar set; Connected component; SELF-SIMILAR SETS; HAUSDORFF DIMENSION; CANTOR SETS; FRACTALS;

D O I：

10.1016/j.jmaa.2011.06.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the Lipschitz equivalence of a class of general Sierpinski carpets in which all non-trivial connected components are line segments. We define a bijection between two link-separated sets with same type by pairing off the basic sets using the indexing by the corresponding symbol space and get a sufficient condition that two general Sierpinski carpets are Lipschitz equivalent. Several examples will be given to illustrate our idea. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：16 / 23

页数：8

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