A Gauss-Kuzmin-type problem for a family of continued fraction expansions
type: Item
instance of: scholarly article
title: A Gauss-Kuzmin-type problem for a family of continued fraction expansions
zbMATH Open document ID: 1319.11049
author: Dan Lascu
published in: Journal of Number Theory
publication date: 2014-04-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1108.3441
review text: The aim of the present paper is to find out a version of the well-known Gauss-Kuzmin type problem for a family of non-regular continued fraction expansions of any number in the unit interval \(I=[0,1]\) with digits which are differences of consecutive non-positive integer powers of any integer \(m\geq 2\) introduced by \textit{H.-C. Chan} [Fibonacci Q. 44, No. 1, 73--84 (2006; Zbl 1204.11032)] following the theory of random systems with complete connections by \textit{M. Iosifescu} and \textit{S. Grigorescu} [Dependence with complete connections and its applications. Cambridge (UK): Cambridge University Press (1990; Zbl 0749.60067); second printing slightly corrected (2009; Zbl 1154.60060)].
Mathematics Subject Classification ID: 11K50
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 37A50
zbMATH DE Number: 6282072
zbMATH Keywords: invariant measure
zbMATH Keywords: Perron-Frobenius operator
zbMATH Keywords: random system with complete connections
reviewed by: Chryssoula Ganatsiou
MaRDI profile type: Publication
OpenAlex ID: W2084852395
arXiv ID: 1108.3441
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DOI: 10.1016/J.JNT.2012.12.007
description: scientific article