一类齐次Moran集的上盒维数

Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (3): 676-683.

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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)

Abstract

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

CLC Number:

O189

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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Upper Box Dimension of a Class of Homogeneous Moran Sets

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