BILIPSCHITZ EMBEDDING OF SELF-SIMILAR SETS

被引：24

作者：

Deng, Juan ^{[2
]}

Wen, Zhi-Ying ^{[2
]}

Xiong, Ying ^{[3
]}

Xi, Li-Feng ^{[1
]}

机构：

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

[2] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

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

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2011年 / 114卷

关键词：

LIPSCHITZ EQUIVALENCE; HAUSDORFF DIMENSION; CONFORMAL SETS; CANTOR SETS; FRACTALS;

D O I：

10.1007/s11854-011-0012-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove that each self-similar set satisfying the strong separation condition can be bilipschitz embedded into each self-similar set with larger Hausdorff dimension. A bilipschitz embedding between two self-similar sets of the same Hausdorff dimension both satisfying the strong separation condition is only possible if the two sets are bilipschitz equivalent.

引用

页码：63 / 97

页数：35

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