POROSITY, DIMENSION, AND LOCAL ENTROPIES: A SURVEY

被引：0

作者：

Shmerkin, Pablo ^{[1
]}

机构：

[1] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England

来源：

REVISTA DE LA UNION MATEMATICA ARGENTINA | 2011年 / 52卷 / 02期

关键词：

ITERATED FUNCTION SYSTEMS; CONICAL UPPER DENSITY; POROUS MEASURES; PACKING DIMENSION; MEAN POROSITY; JULIA SETS; R-N;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will survey the various notions of porosity of sets and measures that have been proposed, and how they relate to dimension. Along the way, we will introduce the idea of local entropy averages, which arose in a different context, and was then applied to obtain a bound for the dimension of mean porous measures.

引用

页码：81 / 103

页数：23

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