分形集的拟一致不连通性

吕凡, 熊瑛, 奚李峰

数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 521-528.

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数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 521-528. DOI: 10.12386/A2015sxxb0053
论文

分形集的拟一致不连通性

    吕凡1, 熊瑛2, 奚李峰3
作者信息 +

Quasi Uniform Disconnectedness of Fractals

    Fan LÜ1, Ying XIONG2, Li Feng XI3
Author information +
文章历史 +

摘要

一致不连通性在分形几何的研究中起重要作用.本文讨论了拟一致不连通性: 对于一类由数列定义的集合,得到其(拟)一致不连通性成立的充要条件; 还引入了一类缓变莫朗集,得到其拟一致不连通性成立的一个充分条件.

Abstract

The uniform disconnectedness plays an important role in the study of fractal geometry. In this paper, we discuss the quasi uniform disconnectedness. For a class of sets defined by sequence, we obtain the necessary and sufficient condition for them to be (quasi) uniformly disconnected. We also introduce Moran sets with slow change and give a sufficient condition to insure their quasi uniform disconnectedness.

关键词

分形集 / 拟一致不连通性 / 莫朗集

Key words

fractal / quasi uniform disconnectedness / Moran set

引用本文

导出引用
吕凡, 熊瑛, 奚李峰. 分形集的拟一致不连通性. 数学学报, 2015, 58(3): 521-528 https://doi.org/10.12386/A2015sxxb0053
Fan LÜ, Ying XIONG, Li Feng XI. Quasi Uniform Disconnectedness of Fractals. Acta Mathematica Sinica, Chinese Series, 2015, 58(3): 521-528 https://doi.org/10.12386/A2015sxxb0053

参考文献

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[11] Xi L. F., Porosity of self-affine sets, Chin. Ann. Math. Ser. B, 2008, 29(3): 333-340.

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[13] Xi L. F., Xiong Y., Self-similar sets with initial cubic patterns, C. R. Math. Acad. Sci. Paris, 2010, 348(1-2): 15-20.

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基金

国家自然科学基金资助项目(11371329, 11471124,11101159);新世纪优秀人才支持计划;浙江省自然科学基金资助项目(LR13A1010001,LY12F02011)

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