自相似集的质量分布原理与Hausdorff测度及其应用

许绍元, 周作领, 苏维宜

数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 117-124.

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PDF(445 KB)
数学学报 ›› 2010, Vol. 53 ›› Issue (1) : 117-124. DOI: 10.12386/A2010sxxb0016
论文

自相似集的质量分布原理与Hausdorff测度及其应用

    许绍元1, 周作领2, 苏维宜3
作者信息 +

On the Mass Distribution Principle and Hausdorff Measure for the Self-Similar Sets and Applications

    Shao Yuan XU1, Zuo Ling ZHOU2, Wei Yi SU3
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文章历史 +

摘要

本文提出了满足开集条件的自相似集的质量分布原理.作为应用,得到了计算一类满足开集条件的自相似集的Hausdorff测度的准确值的方法, 并举例说明了此方法对于计算一类满足开集条件的自相似集的Hausdorff测度的准确值是行之有效的.

 

Abstract

In this paper, the mass distribution principle for the self-similar sets satisfying the open set condition (OSC) is set up. As an application, we obtain a new method for computing the exact value of the Hausdorff measure for a class of self-similar sets satisfying OSC. In addition, we give two examples to show that the new method is effective and workable to compute the exact values of the Hausdorff measures of a class of self-similar sets satisfying OSC.

 

关键词

Hausdorff测度与Hausdorff测度维数 / 自相似集 / 开集条件

Key words

Hausdorff measure and Hausdorff dimension / self-similar sets / open set condition

引用本文

导出引用
许绍元, 周作领, 苏维宜. 自相似集的质量分布原理与Hausdorff测度及其应用. 数学学报, 2010, 53(1): 117-124 https://doi.org/10.12386/A2010sxxb0016
Shao Yuan XU, Zuo Ling ZHOU, Wei Yi SU. On the Mass Distribution Principle and Hausdorff Measure for the Self-Similar Sets and Applications. Acta Mathematica Sinica, Chinese Series, 2010, 53(1): 117-124 https://doi.org/10.12386/A2010sxxb0016

参考文献


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基金

国家自然科学基金资助项目(10961003;10971236)

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