数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 676-683.

• 论文 • 上一篇    下一篇

一类齐次Moran集的上盒维数

张婧茹1(),李彦哲1,*(),娄曼丽2()   

  1. 1 广西大学数学与信息科学学院 南宁 530004
    2 广东技术师范大学数学与系统科学学院 广州 510665
  • 收稿日期:2019-03-18 出版日期:2020-06-26 发布日期:2020-07-15
  • 通讯作者: 李彦哲 E-mail:zjryao@163.com;lyzkbm@163.com;loumanli@126.com
  • 作者简介:张婧茹, E-mail:zjryao@163.com|娄曼丽, E-mail:loumanli@126.com
  • 基金资助:
    国家自然科学基金(11901121);广西自然科学基金(2017GXNSFBA198088);广东自然科学基金(2018A030313971);广东省教育厅项目(2017KTSCX112)

Upper Box Dimension of a Class of Homogeneous Moran Sets

Jingru Zhang1(),Yanzhe Li1,*(),Manli Lou2()   

  1. 1 Colledge of Mathematics and Informnation Science, Guangxi University, Nanning 530004
    2 Department of Mathematics, Guangdong Polytechnic Normal Univercity, Guangzhou 510665
  • Received:2019-03-18 Online:2020-06-26 Published:2020-07-15
  • Contact: Yanzhe Li E-mail:zjryao@163.com;lyzkbm@163.com;loumanli@126.com
  • Supported by:
    the NSFC(11901121);the Guangxi Natural Science Foundation(2017GXNSFBA198088);the Guangdong Natural Science Foundation(2018A030313971);the Education Department Foundation of Guangdong Province(2017KTSCX112)

摘要:

该文利用连通分支与其间隔构造了一类特殊的齐次Moran集:{mk}-拟齐次完全集,并证明该集合在sup{mk}有限的条件下其上盒维数与packing维数可以达到所有齐次Moran集的最小值,并得到该集合在一定条件下上盒维数取值范围,并找到了上盒维数取到精确表达式所需的一个充分条件.

关键词: 齐次Moran集, 拟齐次完全集, 上盒维数

Abstract:

In this paper, we construct a special homogeneous moran set:{mk}-quasi-homogeneous perfect set by the connected components and the gaps, and prove that the upper box dimension and packing dimension of the set can get the maximum value of the homogeneous moran set under the condition sup{mk} < ∞. We also obtain the range of the upper box dimension of the set under some conditions and find a sufficient condition for getting the exact expression of the upper box dimension.

Key words: Homogeneous Moran set, Quasi-homogeneous perfect set, Upper box dimension

中图分类号: 

  • O189