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Quantitative distortion and the Hausdorff dimension of continued fractions

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.

preprint2020arXivOpen access
Daniel Ingebretson
math.DSmath.NT
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Daniel Ingebretson

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