Martin boundary and exit space on the Sierpinski gasket  

作　　者：LAU Ka-Sing NGAI Sze-Man 

机构地区：[1]Department of Mathematics,The Chinese University of Hong Kong [2]Department of Mathematical Sciences,Georgia Southern University

出　　处：《Science China Mathematics》2012年第3期475-494,共20页中国科学：数学（英文版）

摘　　要：We define a new Markov chain on the symbolic space representing the Sierpinski gasket (SG),and show that the corresponding Martin boundary is homeomorphic to the SG while the minimal Martin boundary is the three vertices of the SG.In addition,the harmonic structure induced by the Markov chain coincides with the canonical one on the SG.This suggests another approach to consider the existence of Laplacians on those self-similar sets for which the problem is still not settled.We define a new Markov chain on the symbolic space representing the Sierpinski gasket （SG）,and show that the corresponding Martin boundary is homeomorphic to the SG while the minimal Martin boundary is the three vertices of the SG.In addition,the harmonic structure induced by the Markov chain coincides with the canonical one on the SG.This suggests another approach to consider the existence of Laplacians on those self-similar sets for which the problem is still not settled.

关 键 词：Martin boundary Markov chain Green function harmonic function FRACTAL Sierpinski gasket 

分 类 号：O211.62[理学—概率论与数理统计]