Arithmetic and dynamical properties of the Rauzy fractal
type: Item
instance of: scholarly article
title: Arithmetic and dynamical properties of the Rauzy fractal
zbMATH Open document ID: 0918.11048
author: Ali Messaoudi
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1999-03-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/233819
full work available at URL: jtnb1998-1.html
review text: Explicit measure-theoretic isomorphisms are constructed between the symbolic system associated to the substitution \( \sigma_k:0\mapsto 01, 1\mapsto 02,\dots, k-1\mapsto 0k,k\mapsto 0\) for \(k>2\) and a rotation of the torus, and between the adic stationary system associated to the same substitution and the same rotation. Further, it is shown that the two isomorphisms are continuous everywhere. The proofs involve a careful analysis of the boundary of the fractal set introduced by \textit{G. Rauzy} [Bull. Soc. Math. Fr. 110, 147-178 (1982; Zbl 0522.10032)].
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1229652
zbMATH Keywords: metric isomorphism
zbMATH Keywords: Rauzy fractal
zbMATH Keywords: substitution system
zbMATH Keywords: adic stationary system
reviewed by: Thomas B. Ward
MaRDI profile type: Publication
OpenAlex ID: W2075708776
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DOI: 10.5802/JTNB.223
description: scientific article; zbMATH DE number 1229652