A Gauss-Kuzmin-Lévy theorem for Rényi-type continued fractions
arXiv:1810.10249 · doi:10.4064/aa181009-18-2
Abstract
We consider an interval map which is a generalization of the Rényi 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 Szüsz's method to prove a Gauss-Kuzmin-Lévy-type theorem.
11 pages