Quasi-Lipschitz equivalence of fractals

被引：43

作者：

Xi, Li-Feng ^{[1
]}

机构：

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

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2007年 / 160卷 / 01期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1007/s11856-007-0053-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper proves that if E and F are dust-like C-1 self-conformal sets with 0 < H-H(dim)E (E), H-H(dim)F (F) < infinity, then there exists a bijection f: E -> F such that (dim(H)F) log vertical bar f(x) - f(y)vertical bar/(dim(H)E) log vertical bar x -y vertical bar -> 1 uniformly as vertical bar x-y vertical bar -> 0. It is also proved that a self-similar arc is Hoder equivalent to [0, 1] if and only if it is a quasi-arc.

引用

页码：1 / 21

页数：21