Lipschitz equivalence of fractal sets in a"e

被引：10

作者：

Deng GuoTai ^{[1
]}

He XingGang ^{[1
]}

机构：

[1] Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2012年 / 55卷 / 10期

基金：

中国国家自然科学基金;

关键词：

dust-like; graph-directed iterating function systems; Lipschitz equivalence; self-similar sets; SELF-SIMILAR SETS; HAUSDORFF DIMENSION; CANTOR SETS;

D O I：

10.1007/s11425-012-4444-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let T(q,D) be a self-similar (fractal) set generated by where integer q > 1 and D = {d (1), d (2), aEuro broken vertical bar, d (N) } aS, a"e. To show the Lipschitz equivalence of T(q,D) and a dust-like T(q,C), one general restriction is D aS, a"e by Peres et al. [Israel J Math, 2000, 117: 353-379]. In this paper, we obtain several sufficient criterions for the Lipschitz equivalence of two self-similar sets by using dust-like graph-directed iterating function systems and combinatorial techniques. Several examples are given to illustrate our theory.

引用

页码：2095 / 2107

页数：13

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