Self-similar Sets as Hyperbolic Boundaries

被引：27

作者：

Lau, Ka-Sing ^{[1
]}

Wang, Xiang-Yang ^{[2
]}

机构：

[1] Chinese Univ Hong Kong, Shatin, Hong Kong, Peoples R China

[2] Zhongshan Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2009年 / 58卷 / 04期

关键词：

boundary; geodesic ray; hyperbolic graph; iterated function system; self-similar sets; open set condition; SIERPINSKI GASKET; DIMENSION; FRACTALS;

D O I：

10.1512/iumj.2009.58.3639

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that, for an iterated function system {S-j}(j=1)(N), of similitudes that satisfies the open set condition, there is a natural graph structure in the representing symbolic space to make it a hyperbolic graph, and the hyperbolic boundary is homeomorphic to the self-similar set generated by {S-j}(j=1)(N).

引用

页码：1777 / 1795

页数：19

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