The random continued fraction transformation
Charlene Kalle, Tom Kempton, Evgeny Verbitskiy
TL;DR
This paper introduces a novel random dynamical system combining the Gauss map and Rénnyi continued fraction map, analyzing its properties and the resulting continued fraction expansions.
Contribution
It presents a new random dynamical system for continued fractions, exploring its structure and dynamical behavior, which has not been studied before.
Findings
Characterization of the continued fractions generated by the system
Analysis of the system's dynamical properties
Insights into the statistical behavior of the expansions
Abstract
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the R\'enyi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Chaos control and synchronization