Neil MacVicar

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20232026

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math.DS2026

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

Neil MacVicar

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

math.DS2024

Intersections of Cantor Sets Derived from Complex Radix Expansions

Neil MacVicar

Let $C$ be the attractor of the IFS ${f_{d} (z) = (- n + i)^{- 1} (z + d) : d \in D}$ , $D \subset {0, 1, \dots, n^{2}}$ and let $dim$ denote the box-counting dimension. It is known that…

math.DS2023

Multiplicative Invariance for a Class of Subsets of the Complex Plane

Neil MacVicar

Multiplicative invariance is a well-studied property of subsets of the unit interval. The theory in the complex plane is less developed. This paper introduces an analogous definiti…

On the intersections of homogeneous self-similar sets with their translates in Rn and a formulation of multiplicative invariance in Zn

Intersections of Cantor Sets Derived from Complex Radix Expansions

Multiplicative Invariance for a Class of Subsets of the Complex Plane

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