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arXiv · 2002.10232

Quantitative distortion and the Hausdorff dimension of continued fractions

Daniel Ingebretson
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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.

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Daniel Ingebretson. 2020-02-24. Quantitative distortion and the Hausdorff dimension of continued fractions. https://arxiv.org/abs/2002.10232

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