Conjugacy of \(Z^2\)-subshifts and textile systems
type: Item
instance of: scholarly article
title: Conjugacy of \(Z^2\)-subshifts and textile systems
zbMATH Open document ID: 0970.37016
author: Hiroshi Aso
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2001-10-15T00:00:00Z
review text: The topological conjugacies of one-dimensional Markov-shifts are classified by Williams strong shift equivalence, an equivalence relation of the adjacency matrices. The author extends this to two dimensions for subshifts of finite type (SFT) using textile shifts. These are special SFTs and it is shown, that any SFT is conjugated to a textile shift. Moreover, topological conjugacies of two-dimensional SFTs are shown to be factorizable into finitely many bipartite codes. For textile shifts, bipartite graphs are associated to each of the factors, which yields the above-mentioned result.
Mathematics Subject Classification ID: 37B50
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37C15
zbMATH DE Number: 1501165
zbMATH Keywords: topological conjugacy
zbMATH Keywords: factorization
zbMATH Keywords: bipartite codes
zbMATH Keywords: shift equivalence
reviewed by: Jens D. M. Rademacher
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195143225
OpenAlex ID: W2045616057
cites work: The decomposition theorem for two-dimensional shifts of finite type
cites work: Q4169512
cites work: An Introduction to Symbolic Dynamics and Coding
cites work: Topological conjugacy for sofic systems
cites work: Notes on a class of tiling problems
cites work: Classification of subshifts of finite type
DOI: 10.2977/PRIMS/1195143225
description: scientific article; zbMATH DE number 1501165