The positive topological entropy not equivalent to chaos. A class of subshifts
type: Item
instance of: scholarly article
title: The positive topological entropy not equivalent to chaos. A class of subshifts
zbMATH Open document ID: 0813.54027
author: Gongfu Liao
author: Zuoling Zhou
author: Lan Yu Wang
published in: Science in China. Series A
publication date: 1995-01-16T00:00:00Z
review text: Let \(X\) be a compact metric space and let \(f:X \to X\) be a continuous map. If \(x \neq y\) are points in \(X\) such that \(\limsup d(f^ n(x)\), \(f^ n(y))>0\) and \(\liminf d(f^ n(x), f^ n(y)) = 0\), then \(\{x,y\}\) is called a chaotic pair (for \(f)\). If \(X_ 0\) is an invariant subset of \(X\) which contains an uncountable subset \(D\) such that any two different points in \(D\) form a chaotic pair, then \(f\) is called chaotic on \(X_ 0\) [\textit{T.-Y. Li} and \textit{J. A. Yorke}, Am. Math. Mon. 82, 985-992 (1975; Zbl 0351.92021)]. In the paper under review the authors prove that every one-sided shift contains a chaotic minimal subshift with zero topological entropy.
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 54C70
zbMATH DE Number: 700523
zbMATH Keywords: chaotic dynamical system
zbMATH Keywords: minimal subshift
reviewed by: Luchezar Stoyanov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 700523