The Hausdorff dimension spectrum of Conformal Graph Directed Markov Systems and applications to Nearest Integer continued fractions

TL;DR

This paper investigates the Hausdorff dimension spectrum of two dynamical systems related to the nearest integer continued fraction, demonstrating that both systems possess a full spectrum, which has implications for understanding their fractal geometry.

Contribution

The paper establishes that two specific dynamical systems associated with the nearest integer continued fraction have a full Hausdorff dimension spectrum, a novel result in this context.

Findings

Both systems have full Hausdorff dimension spectrum.

The results apply to the analysis of fractal structures in continued fractions.

Implications for the geometric complexity of these dynamical systems.

Abstract

In this paper, we consider two dynamical systems associated to the nearest integer continued fraction, and show that both of them have full Hausdorff dimension spectrum.