A generalization of a result by W. Li and F. Dekking on the Hausdorff dimension of subsets of self-similar sets with prescribed group frequency of their codings
A generalization of a result by W. Li and F. Dekking on the Hausdorff dimension of subsets of self-similar sets with prescribed group frequency of their codings
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DOI：
10.1007/s00010-006-2831-0
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发表时间：
2006-09
影响因子：
0.8
通讯作者：
L. Olsen
中科院分区：
文献类型：
--
作者：
L. Olsen
设K是不满足开集条件的自相似集。最近，Li和Dekking计算了K中编码中具有规定频率的数字组的点集的Hausdorff维(与Hausdorff维相反，Hausdorff维是指编码中具有规定频率的点的集合)。本文证明了文献[OL1，OL2，OW1，OW2]中发展的散点多重分形分析的方法和技巧可以用来简单地证明这一结果的实质性推广。
LetKbe a self-similar set insatisfying the Open Set Condition. Recently Li and Dekking computed the Hausdorff dimension of the set of points inKwith prescribed frequencies ofgroupsof digits in their codings (as opposed to the Hausdorff dimension the set of points with prescribed frequencies of digits in their codings). In this paper we show that the methods and techniques from multifractal analysis of divergence points developed in [Ol1, Ol2, OW1, OW2] can be applied to give a simple proof of a substantial generalization of this result.