Some skew product transformations associated with continued fractions and their invariant measures
type: Item
instance of: scholarly article
title: Some skew product transformations associated with continued fractions and their invariant measures
zbMATH Open document ID: 0606.10042
author: Shunji Ito
published in: Tokyo Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The paper is a careful study of the ergodic properties of the maps \[ T_ 1(x,y)=(1/x-[1/x], y/x-[y/x])\quad and\quad T_ 2(x,y)=(1/x-[1/x], -y/x-[-y/x]). \] These transformations induce related expansions of irrational numbers y in the form \(y=\sum^{\infty}_{k=1}| \theta (k-1)| b(k),\) and \(y=\sum^{\infty}_{k=1}\theta (k-1) c(k)\) where \(\theta (n)=q_ n x-p_ n\) which are useful for estimating the discrepancy of the sequence \(\{\) nx\(\}\) [see \textit{V. T. Sós}, Top. Number Theory, Debrecen 1974, Colloq. Math. Soc. János Bolyai 13, 359- 367 (1976; Zbl 0354.10028)].
reviewed by: Fritz Schweiger
Mathematics Subject Classification ID: 11K16
Mathematics Subject Classification ID: 11K06
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 3979180
zbMATH Keywords: number theoretical transformations
zbMATH Keywords: skew product transformations
zbMATH Keywords: continued fraction transformation
zbMATH Keywords: ergodic properties
zbMATH Keywords: expansions of irrational numbers
zbMATH Keywords: discrepancy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270150981
OpenAlex ID: W2066700894
DOI: 10.3836/TJM/1270150981
description: scientific article; zbMATH DE number 3979180