由表示系统生成的分形的维数

龙伦海

数学学报 ›› 2001, Vol. 44 ›› Issue (4) : 627-632.

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PDF(443 KB)
数学学报 ›› 2001, Vol. 44 ›› Issue (4) : 627-632. DOI: 10.12386/A2001sxxb0082
论文

由表示系统生成的分形的维数

    龙伦海
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The Hausdorff Dimension of Fractals Generated from Representing System

    Lun Hai LONG
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摘要

在这篇文章里,由Rn中点的表示系统所生成的自仿射集中,给出了自仿射集满足Moran开集条件的一个新的判别方法和不满足开集条件的自相似集的Hausdorff维数的上界和下界,并根据两个实例估计出其上下界是相等的.

Abstract

In this article, in the representing system of Rn, a new criteria for the self-affine sets verifying the Moran's open conditions, the lower and upper bounds for the Hausdorff dimensions of the self-similar sets which is not necessary to verify the open set conditions are given, and using two examples, the equality of the upper lower bounds is estimated.

关键词

开集条件 / Hausdorff维数 / 自相似集 / 表示系统

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龙伦海. 由表示系统生成的分形的维数. 数学学报, 2001, 44(4): 627-632 https://doi.org/10.12386/A2001sxxb0082
Lun Hai LONG. The Hausdorff Dimension of Fractals Generated from Representing System. Acta Mathematica Sinica, Chinese Series, 2001, 44(4): 627-632 https://doi.org/10.12386/A2001sxxb0082
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