一类齐次Moran集的上盒维数

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

一类齐次Moran集的上盒维数

张婧茹¹(),李彦哲^1,*(),娄曼丽²()

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 Li^1,*(),Manli Lou²()

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/Abstract

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：{m_k}-拟齐次完全集，并证明该集合在sup{m_k}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:{m_k}-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{m_k} < ∞. 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

张婧茹,李彦哲,娄曼丽. 一类齐次Moran集的上盒维数[J]. 数学物理学报, 2020, 40(3): 676-683.

Jingru Zhang,Yanzhe Li,Manli Lou. Upper Box Dimension of a Class of Homogeneous Moran Sets[J]. Acta mathematica scientia,Series A, 2020, 40(3): 676-683.

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