THE HAUSDORFF DIMENSION OF THE REGION OF MULTIPLICITY ONE OF OVERLAPPING ITERATED FUNCTION SYSTEMS ON THE INTERVAL

IF 0.5 4区数学 Q3 MATHEMATICS

Osaka Journal of Mathematics Pub Date : 2021-04-01 DOI:10.18910/79428

Kengo Shimomura

引用次数: 1

Abstract

We consider iterated function systems on the unit interval generated by two contractive similarity transformations with the same similarity ratio. When the ratio is greater than or equal to $1/2$, the limit set is the interval itself and the code map is not one-to-one. We study the set of points of the limit set having unique addresses. We obtain a formula for the Hausdorff dimension of the set when the similarity ratio belongs to certain intervals by applying the concept of graph directed Markov system.

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区间上重叠迭代函数系统的多重域的豪斯多夫维数

我们考虑由两个相似率相同的压缩相似变换生成的单位区间上的迭代函数系统。当比率大于或等于$1/2$时，限制集是区间本身，并且代码映射不是一对一的。我们研究了具有唯一地址的极限集的点集。应用图有向马尔可夫系统的概念，得到了当相似率属于一定区间时集合的Hausdorff维数的一个公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Osaka Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.