Syndetic sensitivity in semiflows
type: Item
instance of: scholarly article
title: Syndetic sensitivity in semiflows
zbMATH Open document ID: 1354.37022
author: Alica Miller
author: Chad Money
published in: Topology and its Applications
publication date: 2015-11-16T00:00:00Z
review text: It is well known that the Devaney's definition of chaos from 1989 initially had one redundant condition; this fact was proven by \textit{J. Banks} et al. [Am. Math. Mon. 99, No. 4, 332--334 (1992; Zbl 0758.58019)]. Since that time, many authors have published results in this spirit, showing that transitivity and density of periodic points (or variants thereof) imply sensitive dependence on initial conditions (in one sense or another). This article analyses this problem in the context of semiflows given by actions of abelian unital topological semigroups. It generalizes two previous results by other authors. The main result of the paper is the following: If a syndetically transitive semiflow is not minimal, then it is syndetically sensitive.
reviewed by: Marcin Kulczycki
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 6509429
zbMATH Keywords: semiflow
zbMATH Keywords: chaos
zbMATH Keywords: Devaney chaos
zbMATH Keywords: transitivity
zbMATH Keywords: syndetic transitivity
zbMATH Keywords: periodic points
zbMATH Keywords: sensitivity
MaRDI profile type: Publication
full work available at URL: j.topol.2015.09.008
OpenAlex ID: W1787193075
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DOI: 10.1016/J.TOPOL.2015.09.008
description: scientific article; zbMATH DE number 6509429