Graphs induced by iterated function systems

被引：10

作者：

Wang, Xiang-Yang ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

来源：

MATHEMATISCHE ZEITSCHRIFT | 2014年 / 277卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

Hyperbolic graph; Hyperbolic boundary; Iterated function system; Self-similar sets; Open set condition; Weak separation condition; SELF-SIMILAR SETS; WEAK SEPARATION CONDITION; SIERPINSKI GASKET; MARTIN BOUNDARY; HYPERBOLIC BOUNDARIES; RANDOM-WALKS; KERNELS;

D O I：

10.1007/s00209-014-1280-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an iterated function system (IFS) of similitudes, we define two graphs on the representing symbolic space. We show that if the self-similar set has positive Lebesgue measure or the IFS satisfies the weak separation condition, then the graphs are hyperbolic; moreover the hyperbolic boundaries are homeomorphic to the self-similar sets.

引用

页码：829 / 845

页数：17

共 26 条

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