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.
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页码：1 / 21
页数：21
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