Various expansive measures for flows
type: Item
instance of: scholarly article
title: Various expansive measures for flows
zbMATH Open document ID: 1410.54042
author: Ngoc-Thach Nguyen
author: Keonhee Lee
author: C. A. Morales
published in: Journal of Differential Equations
publication date: 2018-05-28T00:00:00Z
review text: The paper under review is a very nice work which presents a characterization of countably expansive flows in measure-theoretical terms as in the discrete case. The authors define the notion of countably expansive flows and prove that a homeomorphism of a compact metric space is countable expansive just when its suspension flow is. Apart from that, in this work are presented several examples. A measure-expansive flow which is not countably expansive is constructed. Moreover, a definition for weak expansive measures for flows is presented, too. It is proved that a flow of a compact metric space is countable expansive if and only if it is weak measure-expansive (i.e. every orbit-vanishing measure is weak expansive). It is noticed that unlike the measure-expansive ones, the weak measure-expansive flows may exist on closed surfaces. To finish, it is proved that the integrated flow of a \(C^1\) vector field on a compact smooth manifold is \(C^1\) stably expansive if and only if it is \(C^1\) stably weak measure-expansive.
reviewed by: Juan L. G. Guirao
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37B05
zbMATH DE Number: 6875572
zbMATH Keywords: expansive homeomorphism
zbMATH Keywords: expansive measure
zbMATH Keywords: countably expansive
MaRDI profile type: Publication
full work available at URL: j.jde.2018.04.036
OpenAlex ID: W2802696722
cites work: Singular cw-expansive flows
cites work: A note on measure-expansive diffeomorphisms
cites work: Expansive one-parameter flows
cites work: Expansive measures for flows
cites work: Weak measure expansive flows
cites work: \(C^1\)-stably expansive flows
cites work: Vector fields with topological stability
cites work: Q5710724
cites work: Unstable Homeomorphisms
Wikidata QID: Q129931975
DOI: 10.1016/J.JDE.2018.04.036
description: scientific article; zbMATH DE number 6875572