Tilings, substitution systems and dynamical systems generated by them
type: Item
instance of: scholarly article
title: Tilings, substitution systems and dynamical systems generated by them
zbMATH Open document ID: 0745.52013
DOI: 10.1007/BF02793412
published in: Journal d'Analyse Mathématique
publication date: 1992-06-25T00:00:00Z
review text: The tiling problem is the question whether, given a finite set of unit square domain tiles with certain adjacency rules (``tiling system''), there exists a tiling of the entire plane using copies of these tiles: this problem has been proved undecidable by Berger. The author of the paper under review associates to a tiling system a dynamical system consisting of all tilings of the planes using this tiling system with the natural action of \(\mathbb{Z}^ 2\) by translations. He addresses the question of checking what classes of dynamical systems can be realized this way. He studies in particular relations between \(2-D\) substitution systems and tiling systems from the point of view of dynamical systems, giving several nice examples. Finally he sketches a new proof of the undecidability of the tiling problem.
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 03D05
Mathematics Subject Classification ID: 28D99
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 3961
zbMATH Keywords: tiling system
zbMATH Keywords: dynamical system
zbMATH Keywords: substitution systems
zbMATH Keywords: undecidability of the tiling problem
author: Shahar Mozes
reviewed by: Jean-Paul Allouche
MaRDI profile type: Publication
Wikidata QID: Q56443068
cites work: The undecidability of the domino problem
cites work: Minimal flows arising from substitutions of non-constant length
cites work: Q4744504
cites work: Undecidability and nonperiodicity for tilings of the plane
full work available at URL: https://doi.org/10.1007/bf02793412
OpenAlex ID: W2057301059
description: scientific article; zbMATH DE number 3961