若干个齐次对称康托集的交

张云秀, 顾惠

数学学报 ›› 2011, Vol. 54 ›› Issue (6) : 1043-1048.

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数学学报 ›› 2011, Vol. 54 ›› Issue (6) : 1043-1048. DOI: 10.12386/A2011sxxb0103
论文

若干个齐次对称康托集的交

    张云秀1, 顾惠2
作者信息 +

Intersection of Homogeneous Symmetric Cantor Set with Its Translations

    Yun Xiu ZHANG1, Hui GU2
Author information +
文章历史 +

摘要

Γ是齐次对称康托集, 对 n 个实数 t1,...,tn 讨论了交集Γ ∩(Γ+t1)∩...∩(Γ+ tn)≠ Ø的条件,以及计算出Γ ∩(Γ+t1)∩...∩(Γ+ tn)的 Hausdorff 维数的精确表达式.  

Abstract

Let Γ be the homogeneous symmetric cantor set. For n real numbers t1, ..., tn, the condition for the intersection Γ∩(Γ+t1) ∩ ...,∩(Γ+tn)≠ Ø is discussed and the exact Hausdorff dimension of Γ∩(Γ+t1) ∩ ...,∩(Γ+tn) is computed.  

关键词

齐次对称康托集 / 交集 / 莫朗集

Key words

homogeneous symmetric cantor set / intersection / Moran sets

引用本文

导出引用
张云秀, 顾惠. 若干个齐次对称康托集的交. 数学学报, 2011, 54(6): 1043-1048 https://doi.org/10.12386/A2011sxxb0103
Yun Xiu ZHANG, Hui GU. Intersection of Homogeneous Symmetric Cantor Set with Its Translations. Acta Mathematica Sinica, Chinese Series, 2011, 54(6): 1043-1048 https://doi.org/10.12386/A2011sxxb0103

参考文献

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[7] Li W., Yao Y., Zhang Y., Self-similar structure on intersection of homogeneous symmetric Cantor sets, Mathematische Nachrichten, 2009, 195: 113-125.

[8] Wen Z. Y., Mathematical Foundations of Fractal Geometry, Shanghai: Shanghai Science and Technology Press, 1999.

[9] Wen Z. Y., Moran sets and Moran classes, Chinese Sci. Bull., 2001, 46: 1849-1856.

[10] Falconer K. J., Fractal Geometry-Mathematical Foundations and Applications, Chichester: John Wiley & Sons Ltd., 1990.

[11] Pertti M., Geometry of sets and Measures in Euclidean Space: Fractals and Rectifiability, Cambridge: Cambridge University Press, 1995.

基金

上海市自然科学基金项目(11ZR1410300); 南京林业大学科技创新基金项目(163101043)

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