A transfer property in Diophantine approximation
type: Item
instance of: scholarly article
title: A transfer property in Diophantine approximation
zbMATH Open document ID: 1065.37005
author: Patrick Bernard
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2005-01-03T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73612
review text: The author investigates the well-known link between the properties of uniform simultaneous rational approximations for a vector \(w\) in \(\mathbb{R}^n\) and the sequence of best simultaneous rational approximations for such a vector \(w\). The study makes use of a dynamical framework. In particular, the quality of the best simultaneous rational approximations to the vector \(w\) is expressed in terms of the best return times near the origin for the translation \(x\mapsto x+ w\) on the \(n\)-dimensional torus.
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 11J13
Mathematics Subject Classification ID: 37C05
zbMATH DE Number: 2124648
zbMATH Keywords: diophantine approximation
zbMATH Keywords: ergodic translations
zbMATH Keywords: return times
reviewed by: Boris Adamczewski
MaRDI profile type: Publication
OpenAlex ID: W1972095553
cites work: Q3222326
cites work: Complex analysis and convolution operators
cites work: Diophantine approximation
DOI: 10.5802/AFST.1057
description: scientific article; zbMATH DE number 2124648