Comparison of various continued fraction expansions: a Lochs-type approach

Dan Lascu, Gabriela Ileana Sebe

Published 2020-05-01Version 1

We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Loch's theorem from 1964. Thus, we aimed to compare the effectiveness of Chan's continued fractions, $\theta-$expansions, $N-$continued fractions and R\'enyi-type continued fractions. A central role in fulfilling our goal is the entropy of the measure preserving transformations which generate these expansions.