A Gauss-Kuzmin theorem for the Rosen fractions
type: Item
instance of: scholarly article
title: A Gauss-Kuzmin theorem for the Rosen fractions
zbMATH Open document ID: 1067.11044
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2005-06-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/93870
review text: Using the natural extensions for the Rosen maps, the author gives an infinite order-chain representation of the sequence of incomplete quotients of the Rosen fractions. She shows that the random systems with complete connections associated with the Rosen continued fraction expansion are with contraction and their transition operators are regular with respect to the Banach space of Lipschitz functions. This leads to a solution of a version of the Gauss-Kuzmin problem for the Rosen fractions.
reviewed by: Takao Komatsu
Mathematics Subject Classification ID: 11K50
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 2184606
zbMATH Keywords: Rosen fractions
zbMATH Keywords: Gauss-Kuzmin theorem
author: Gabriela Ileana Sebe
MaRDI profile type: Publication
OpenAlex ID: W2328315682
cites work: Natural extensions for the Rosen fractions
cites work: Backward Continued Fractions and their Invariant Measures
cites work: The Hurwitz Constant and Diophantine Approximation on Hecke Groups
cites work: Q4273561
cites work: Q4264678
cites work: Q3995207
cites work: Diophantine approximation on Hecke groups
cites work: Q3139670
cites work: Metrical theory for a class of continued fraction transformations and their natural extensions
cites work: Q4891864
cites work: A class of continued fractions associated with certain properly discontinuous groups
cites work: Hecke groups and continued fractions
cites work: Q3140901
DOI: 10.5802/JTNB.381
description: scientific article; zbMATH DE number 2184606