A construction of multiply Xiong chaotic set with full topological entropy for \(\beta\)-transformation
type: Item
instance of: scholarly article
title: A construction of multiply Xiong chaotic set with full topological entropy for \(\beta\)-transformation
zbMATH Open document ID: 1480.37030
author: Yuanfen Xiao
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-07-23T00:00:00Z
review text: Given a topological dynamical system \((X, f)\), a subset \(E\subset X\) containing at least two points is defined to be a Xiong chaotic set if for any subset \(F\subset E\) and any continuous function \(g: F \rightarrow X\), there exists an increasing sequence \(\{q_{k}\}^{\infty}_{k=1}\) of positive integers such that for every \(x\in F\), \(\lim\limits_{k\rightarrow +\infty}f^{q_k}(x)=g(x)\). Two significant results here obtained are as follows. (1) For positively expansive systems with specification property, the authors construct a multiply Xiong chaotic set with full topological entropy everywhere; (2) Although a \(\beta\)-transformation is neither continuous nor satisfies the specification property for all \(\beta>1\), it is possible to construct a Xiong chaotic set with full topological entropy.
reviewed by: Meirong Zhang
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 37B05
zbMATH DE Number: 7374583
zbMATH Keywords: Xiong chaotic set
zbMATH Keywords: topological entropy
zbMATH Keywords: \(\beta\)-transformation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125314
OpenAlex ID: W3163364997
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DOI: 10.1016/J.JMAA.2021.125314
description: scientific article; zbMATH DE number 7374583