Coding of a translation of the two-dimensional torus
type: Item
instance of: scholarly article
title: Coding of a translation of the two-dimensional torus
zbMATH Open document ID: 1171.37009
author: Nicolas Chevallier
published in: Monatshefte für Mathematik
publication date: 2009-06-30T00:00:00Z
review text: A symbolic coding of the ergodically acting map \(T:x\to x+\alpha\), where \(\alpha\in {\mathbb T}^2\) (\({\mathbb T}^2={\mathbb R}^2 /{\mathbb Z}^2\) is the 2D-torus) is presented. It shares several properties with the Sturmian coding os a one-dimensional translation. Such obtained symbolic dynamical system is metrically isomorphic to \(({\mathbb T}^2,\, T)\). The coding is of quadratic growth complexity and 2-balanced.
reviewed by: Ljubiša Kocić
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 11K60
zbMATH DE Number: 5571618
zbMATH Keywords: irrational translation
zbMATH Keywords: coding
zbMATH Keywords: simultaneous Diophantiene approximation
MaRDI profile type: Publication
full work available at URL: s00605-008-0074-y
OpenAlex ID: W2062456323
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DOI: 10.1007/S00605-008-0074-Y
description: scientific article; zbMATH DE number 5571618