Are there chaotic tilings!
type: Item
instance of: scholarly article
title: Are there chaotic tilings!
zbMATH Open document ID: 0790.28011
DOI: 10.1007/BF02098297
author: Daniel Berend
author: Charles Radin
published in: Communications in Mathematical Physics
publication date: 1993-06-29T00:00:00Z
review text: The existence of substitutions with a non-empty continuous spectrum, or even without discrete spectrum at all, has been somehow a surprise for physicists after they began using substitutions, inspired by the Fibonacci sequence, in relation with quasicrystals. The paper under review will, I guess, be also suprising: the authors explore a more subtle use of substitutions to construct tiling dynamical systems without discrete spectrum. Roughly speaking, they make use of a technique of \textit{S. Mozes} [J. Anal. Math. 53, 139-186 (1989; Zbl 0745.52013)], and of the particular substitution (which might look simple at first glance!): \[ \begin{aligned} 0 &\longrightarrow 0\;1\;0\;1\\ 1 &\longrightarrow 1\;1\;1\;0.\end{aligned} \] {}.
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 52C22
Mathematics Subject Classification ID: 82B99
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 11B85
zbMATH DE Number: 222069
zbMATH Keywords: statistical mechanics
zbMATH Keywords: automata sequences
zbMATH Keywords: spectrum
zbMATH Keywords: tiling dynamical systems
reviewed by: Jean-Paul Allouche
MaRDI profile type: Publication
cites work: Mixing properties of substitutions
cites work: Tilings, substitution systems and dynamical systems generated by them
cites work: Substitution dynamical systems - spectral analysis
cites work: Global order from local sources
cites work: DISORDERED GROUND STATES OF CLASSICAL LATTICE MODELS
cites work: Space tilings and local isomorphism
cites work: Q4237498
description: scientific article; zbMATH DE number 222069