POST-CRITICALLY FINITE FRACTAL AND MARTIN BOUNDARY

被引：0
|
作者：
Ju, Hongbing [1 ]
Lau, Ka-Sing [1 ]
Wang, Xiang-Yang [2 ]
机构：
[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
[2] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 364卷 / 01期
关键词：
Fractals; Green function; harmonic functions; monocyclic; post critically finite; Martin boundary; transition probability; SELF-SIMILAR SETS; SIERPINSKI GASKET;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For an iterated function system (IFS), which we call simple post critically finite, we introduce a Markov chain on the corresponding symbolic space and study its boundary behavior. We carry out some fine estimates of the Martin metric and use them to prove that the Martin boundary can be identified with the invariant set (fractal) of the IFS. This enables us to bring in the boundary theory of Markov chains and the discrete potential theory on this class of fractal sets.
引用
收藏
页码：103 / 118
页数：16
相关论文
共 50 条
12345