Self-similar sets with initial cubic patterns

被引：55

作者：

Xi, Li-Feng ^{[1
]}

Xiong, Ying ^{[2
]}

机构：

[1] Zhejiang Wanli Univ, Inst Math, Ningbo 315100, Zhejiang, Peoples R China

[2] S China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China

来源：

COMPTES RENDUS MATHEMATIQUE | 2010年 / 348卷 / 1-2期

关键词：

LIPSCHITZ EQUIVALENCE; HAUSDORFF DIMENSION; CANTOR SETS;

D O I：

10.1016/j.crma.2009.12.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For A subset of {0, ..., n - 1}(m), let E(A) be the unique nonempty compact subset of R(m) such that E(A) = boolean OR(a is an element of A) (1/nE(A) + a/n). We show that two such self-similar sets E(A) and E(B) (for A, B subset of {0, ..., n - 1}(m)), supposed to be totally disconnected, are Lipschitz equivalent if and only if #A = #B. (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：15 / 20

页数：6

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