Self-affine tiling via substitution dynamical systems and Rauzy fractals.
type: Item
instance of: scholarly article
title: Self-affine tiling via substitution dynamical systems and Rauzy fractals.
zbMATH Open document ID: 1048.37015
author: Yang Wang
author: Víctor F. Sirvent
published in: Pacific Journal of Mathematics
publication date: 2003-02-13T00:00:00Z
review text: \textit{G. Rauzy} [Bull. Soc. Math. Fr. 110, 147--178 (1982; Zbl 0522.10032)] associated a fractal tiling of \(\mathbb R^d\) to a primitive unimodular Pisot substitution. Here, it is shown that the resulting fractal is the closure of its interior, and that a natural decomposition of the Rauzy fractal is a self-affine multitiling. This gives a construction of many aperiodic self-affine tilings. The sets arising in the above decomposition are conjectured to be measure-wise disjoint. A different proof of a theorem by \textit{P. Arnoux} and \textit{S. Ito} [Bull. Belg. Math. Soc. - Simon Stevin 8, 181--207 (2001; Zbl 1007.37001)] concerning a special case of this conjecture is presented.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 37B50
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 52C23
zbMATH DE Number: 1868195
zbMATH Keywords: Rauzy fractal
zbMATH Keywords: self-affine tiling
MaRDI profile type: Publication
full work available at URL: pjm.2002.206.465
OpenAlex ID: W2025774179
DOI: 10.2140/PJM.2002.206.465
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description: scientific article; zbMATH DE number 1868195