Hausdorff dimension and upper box dimension of a class of homogeneous Moran sets

ABSTRACT

In this paper, we construct a class of special homogeneous Moran sets which is called the $\left\{m_k\right\}$-homogeneous Moran sets by the connected components, and obtain the Hausdorff dimension and the upper box dimension of the $\left\{m_k\right\}$-homogeneous Moran sets under some conditions.

KEYWORDS:

• Homogeneous Moran sets
• $\left\{m_k\right\}$-homogeneous Moran sets
• Hausdorff dimension
• upper box dimension
• connected components

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 28A78
• 28A80

Acknowledgments

The authors thank the reviewers for their helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by National Natural Science Foundation of China (No. 11901121), Guangxi Natural Science Foundation (2020GXNSFAA297040), and the special foundation for Guangxi Ba Gui Scholars.