Inhomogeneous self-similar sets and box dimensions

被引：17
|
作者：
Fraser, Jonathan M. [1 ]
机构：
[1] Univ St Andrews, Math Inst, St Andrews KY16 9SS, Fife, Scotland
来源：
STUDIA MATHEMATICA | 2012年 / 213卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
inhomogeneous self-similar set; box dimension; covering regularity exponent;
D O I：
10.4064/sm213-2-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than upper box dimension, Hausdorff dimension and packing dimension.
引用
收藏
页码：133 / 156
页数：24
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