Assouad type dimensions of homogeneous Moran sets and Cantor-like sets

Abstract

In this paper, we give the Assouad dimension formula and the upper bound of the lower dimension for homogeneous Moran sets under the condition $\sup_{k\ge 1}\{n_{k}\}<+\infty$. We also give the Assouad spectrum and the lower spectrum formulas for Cantor-like sets.