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arXiv · 1810.10249

A Gauss-Kuzmin-L\'evy theorem for R\'enyi-type continued fractions

Dan Lascu·Gabriela Ileana Sebe
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Abstract

We consider an interval map which is a generalization of the R\'enyi transformation. For the continued fraction expansion arising from this transformation, we prove a result concerning the asymptotic behavior of the distribution functions of this map. More exactly, we use Sz\"usz's method to prove a Gauss-Kuzmin-L\'evy-type theorem.

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Dan Lascu, Gabriela Ileana Sebe. 2018-10-24. A Gauss-Kuzmin-L\'evy theorem for R\'enyi-type continued fractions. https://doi.org/10.4064/aa181009-18-2

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