Quantitative distortion and the Hausdorff dimension of continued fractions
Number Theory
2020-02-25 v1 Dynamical Systems
Abstract
We prove a quantitative distortion theorem for iterated function systems that generate sets of continued fractions. As a consequence, we obtain upper and lower bounds on the Hausdorff dimension of any set of real or complex continued fractions. These bounds are solutions to Moran-type equations in the convergents that can be easily implemented in a computer algebra system.
Keywords
Cite
@article{arxiv.2002.10232,
title = {Quantitative distortion and the Hausdorff dimension of continued fractions},
author = {Daniel Ingebretson},
journal= {arXiv preprint arXiv:2002.10232},
year = {2020}
}
Comments
14 pages