On the intersections of homogeneous self-similar sets with their translates in ${\mathbb{R}}^n$ and a formulation of multiplicative invariance in ${\mathbb{Z}}^n$

Neil MacVicar

This thesis generalizes the study of $C\cap (C+\alpha )$ where $C$ is the middle third Cantor set to self-affine sets in ${\mathbb{R}}^n$. We present sufficient and necessary conditions…