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中国科学院大学学报 ›› 2013, Vol. 30 ›› Issue (4): 443-449.DOI: 10.7523/j.issn.2095-6134.2013.04.003

• 数学 • 上一篇    下一篇

关于图有向自保形分形的开集条件

郑水草   

  1. 中国科学院大学数学科学学院, 北京 100049; 集美大学理学院, 福建 厦门 361021
  • 收稿日期:2012-03-01 修回日期:2012-10-22 发布日期:2013-07-15
  • 通讯作者: 郑水草
  • 基金资助:

    Supported by the National Natural Science Foundation of China (11171342) 

On the open set condition of the graph directed self-conformal fractals

ZHENG Shui-Cao   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China; School of Sciences, Jimei University, Xiamen 361021, Fujian, China
  • Received:2012-03-01 Revised:2012-10-22 Published:2013-07-15

摘要:

获得关于图有向自保形分形的开集条件的一些等价条件. 特别地,对于这种类型的分形集,给出开集条件和强开集条件是等价的结论.

关键词: 自保形分形, 开集条件, 豪斯道夫测度

Abstract:

In this paper, some conditions equivalent to the open set condition of the graph directed self-conformal fractals are obtained. Especially, it is proven that the strong open set condition and the open set condition are equivalent for such a fractal.

Key words: self-conformal fractal, open set condition, Hausdorff measure

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