Devaney's and Li-Yorke's chaos in uniform spaces
type: Item
instance of: scholarly article
title: Devaney's and Li-Yorke's chaos in uniform spaces
zbMATH Open document ID: 1384.54020
author: Tatsuya Arai
published in: Journal of Dynamical and Control Systems
publication date: 2018-03-01T00:00:00Z
review text: Let \(X\) be a second countable Baire Hausdorff uniform space without isolated points. The following is the main result in this paper. Theorem. Let \(G\) be an Abelian group on \(X\). If a continuous action of \(G\) on \(X\) is chaotic in the Devaney sense, then there exists an uncountable dense scrambled set; so that, it is chaotic in the Li-Yorke sense. Further aspects occasioned by these developments are also discussed.
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B05
zbMATH DE Number: 6845714
zbMATH Keywords: uniform space
zbMATH Keywords: group action
zbMATH Keywords: Devaney chaos
zbMATH Keywords: Li-Yorke chaos
MaRDI profile type: Publication
full work available at URL: s10883-017-9360-0
OpenAlex ID: W2581878745
cites work: On Devaney's Definition of Chaos
cites work: On Li-Yorke pairs
cites work: Sensitivity and Devaney's chaos in uniform spaces
cites work: Topological transitivity and mixing notions for group actions
cites work: Q3993502
cites work: Devaney's chaos or 2-scattering implies Li-Yorke's chaos
cites work: Period Three Implies Chaos
cites work: Chaotic actions of topological semigroups
DOI: 10.1007/S10883-017-9360-0
description: scientific article; zbMATH DE number 6845714