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arXiv · 2005.00380

A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms

Dan Lascu·Gabriela Ileana Sebe
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Abstract

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aimed to compare the efficiency by describing the rate at which the digits of one number-theoretic expansion determine those of another. We study Chan's continued fractions, $\theta$-expansions, $N$-continued fractions and R\'enyi-type continued fractions. A central role in fulfilling our goal is played by the entropy of the absolutely continuous invariant probability measures of the associated dynamical systems.

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Dan Lascu, Gabriela Ileana Sebe. 2020-05-01. A Lochs-Type Approach via Entropy in Comparing the Efficiency of Different Continued Fraction Algorithms. https://arxiv.org/abs/2005.00380

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