Sierpinski地毯上自相似测度以及Markov测度的加倍性质  

Doubling properties of self-similar measures and Markov measures on Sierpinski carpets

作　　者：栗慧[1] 危纯 文胜友[1] 

机构地区：[1]湖北大学数学与统计学学院,武汉430062 [2]华中科技大学数学与统计学院,武汉430074

出　　处：《中国科学：数学》2016年第2期169-182,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11271114和11301162)资助项目

摘　　要：众所周知,当自相似集满足强分离条件时,其上的自相似测度都是加倍的.本文进一步证明在强分离条件下,自相似集上的Markov测度都是加倍的.随后,本文讨论了Sierpinski地毯S上自相似测度及Markov测度的加倍性质.当S不满足强分离条件时,将S分为不同的类型,完全刻画了S上加倍的自相似测度及加倍的Markov测度.As is well known, when a self-similar set satisfies the strong separation condition, all self-similar measures are doubling. In this paper, we further prove that all Markov measures are doubling on a self-similar set with the strong separation condition. Subsequently, we focus on self-similar measures and Markov measures on Sierpinski carpets. Without the strong separation condition, Sierpinski carpets can be divided into different types. In each case, we fully characterize doubling self-similar measures and doubling Markov measures on a Sierpifiski carpet.

关 键 词：SIERPINSKI地毯 加倍性质 自相似测度 Markov测度 

分 类 号：O174.12[理学—数学]