Quantitative distortion and the Hausdorff dimension of continued fractions

2020/02/24 by Daniel Ingebretson, Ingebretson, Daniel
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2002.10232

openalex publication_date 2020/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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