Hausdorff dimensions of affine multiplicative subshifts

Jung-Chao Ban, Wen-Guei Hu, Guan-Yu Lai, Lingmin Liao

Abstract

We calculate the Minkowski and Hausdorff dimensions of affine multiplicative subshifts on $\mathbb{N}$.

Hausdorff dimensions of affine multiplicative subshifts

Abstract

We calculate the Minkowski and Hausdorff dimensions of affine multiplicative subshifts on

.

Paper Structure (4 sections, 7 theorems, 106 equations)

This paper contains 4 sections, 7 theorems, 106 equations.

Table of Contents

Introduction
Proof of Theorem \ref{['Thm: 1']}
Proof of Theorem \ref{['Thm: 3']}
Higher-order interaction

Key Result

Theorem 1.1

Let $q\geq 2$ be an integer and $A$ be an $m\times m$ primitive binary matrix.

Theorems & Definitions (11)

Theorem 1.1: Kenyon et al. kenyon2012hausdorff, Theorem 1.3
Theorem 1.2: Minkowski dimension
Theorem 1.3: Hausdorff dimension
proof : Proof of Theorem \ref{['Thm: 1']}
Lemma 3.1: Billingsley's lemma
Proposition 3.2: Lower bound
proof
Lemma 3.3: Hölder Inequality
proof : Proof of Theorem \ref{['Thm: 3']}
Theorem 4.1
...and 1 more