A dependence with complete connections approach to generalized Rényi continued fractions

We introduce and study in detail a special class of backward continued fractions that represents a generalization of Rényi continued fractions. We investigate the main metrical properties of the digits occurring in these expansions and we construct the natural extension for the transformation that g...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2020-04, Vol.160 (2), p.292-313
Main Authors: Lascu, D., Sebe, G. I.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We introduce and study in detail a special class of backward continued fractions that represents a generalization of Rényi continued fractions. We investigate the main metrical properties of the digits occurring in these expansions and we construct the natural extension for the transformation that generates the Rényi-type expansion. We also define the random system with complete connections associated with the underlying dynamical system whose ergodic behaviour allows us to prove a variant of Gauss–Kuzmin-type theorem.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-019-00974-x