莫朗集的拟Lipschitz等价

汪沁

数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 187-196.

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数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 187-196. DOI: 10.12386/A2013sxxb0019
论文

莫朗集的拟Lipschitz等价

    汪沁
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Quasi-Lipschitz Equivalence of Moran Fractals

    Qin WANG
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摘要

讨论满足c*>0及s*=s*∈(0,1)条件的莫朗集, 并得到如下结论:任意两个该类型莫朗集彼此拟Lipschitz等价当且仅当它们的Hausdorff维数相等.

Abstract

We consider the class of Moran sets satisfying the conditions c*>0 and s*=s*∈(0, 1). We obtain that two Moran fractals in the class are quasi-Lipschitz equivalent if and only if they have the same Hausdorff dimension.

关键词

分形 / 莫朗集 / 拟Lipschitz等价

Key words

fractal / Moran set / quasi-Lipschitz equivalence

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汪沁. 莫朗集的拟Lipschitz等价. 数学学报, 2013, 56(2): 187-196 https://doi.org/10.12386/A2013sxxb0019
Qin WANG. Quasi-Lipschitz Equivalence of Moran Fractals. Acta Mathematica Sinica, Chinese Series, 2013, 56(2): 187-196 https://doi.org/10.12386/A2013sxxb0019

参考文献

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基金

国家自然科学基金(11071224);新世纪优秀人才支持计划;浙江省自然科学基金(LY12F02011)

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