Self-similar sets with initial cubic patterns

被引：53
|
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
收藏
页码：15 / 20
页数：6
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