Lipschitz equivalence of self-similar sets with two-state neighbor automaton

被引：11

作者：

Zhu, Yunjie ^{[1
]}

Yang, Yamin ^{[2
]}

机构：

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

[2] Huazhong Agr Univ, Coll Sci, Inst Appl Math, Wuhan 430070, Hubei, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 458卷 / 01期

关键词：

Lipschitz equivalent; Self-similar sets; Neighbor automaton; Ray-separation condition; p-uniform fractals; CANTOR SETS; FRACTAL SQUARES;

D O I：

10.1016/j.jmaa.2017.09.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The study of Lipschitz equivalence of fractals is a very active topic in recent years, but there are very few results on fractals which is not totally disconnected. In this paper, using finite state automata and the angle separation property, we prove that for a class of self-similar sets with two-state neighbor automaton, two elements are Lipschitz equivalent if and only if they have the same Hausdorff dimension. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：379 / 392

页数：14

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