Some Dimensional Results of a Class of Homogeneous Moran Sets

Abstract

In this paper, we construct a class of special homogeneous Moran sets: $\left\{m_k\right\}$ -quasi-homogeneous perfect sets, and obtain the Hausdorff dimension of the sets under some conditions. We also prove that the upper box dimension and the packing dimension of the sets can get the maximum value of the homogeneous Moran sets under the condition ${\sup }_{k\ge 1}{m}_k<\infty$ and estimate the upper box dimension of the sets in two cases.