Generalization of a theorem of Kusmin
type: Item
instance of: scholarly article
title: Generalization of a theorem of Kusmin
zbMATH Open document ID: 0819.11028
DOI: 10.1007/BF01305774
published in: Monatshefte für Mathematik
publication date: 1994-10-09T00:00:00Z
full work available at URL: https://eudml.org/doc/178657
review text: A generalization of the Gauss-Kuzmin theorem in the metrical theory of continued fractions is given. The generalization is to consider instead of the map of the unit-interval to itself defined by the transformation \(Tx= \sum(k^{-1}- (k+x)^{-1})\), the map of the unit-interval to itself by the transformation \(T(x,y)= (Tx, x/(1- xTx+ xy))\). The main result of the paper is that the probability density function of the above transformation is \((\log 2)^{-1} (1+ xy)^{-2}\).
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 650849
zbMATH Keywords: generalization of Gauss-Kuzmin theorem
zbMATH Keywords: map of unit-interval to itself
zbMATH Keywords: metrical continued fractions
zbMATH Keywords: transformation
zbMATH Keywords: probability density function
author: K. Dajani
author: Cor Kraaikamp
MaRDI profile type: Publication
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OpenAlex ID: W2047948978
description: scientific article; zbMATH DE number 650849