On the topology of the chain recurrent set of a dynamical system

On the topology of the chain recurrent set of a dynamical system

n this paper we associate a pseudo-metric to a dynamical system on a compact metric space. We show that this pseudo-metric is identically zero if and only if the system is chain transitive. If we associate this pseudo-metric to the identity map, then we can present a  characterization for connected...

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Bibliographic Details
Main Author: Seyyed Alireza Ahmadi
Format: Article
Language:English
Published: Universitat Politècnica de València 2014-06-01
Series:Applied General Topology
Subjects:
chain recurrent
chain transitive
chain component
inverse limit space.
Online Access:http://polipapers.upv.es/index.php/AGT/article/view/3050
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spelling doaj-2d85d3048a2a46df8e0c4cece2f7a4202020-11-25T00:49:53ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472014-06-0115216717410.4995/agt.2014.30502552On the topology of the chain recurrent set of a dynamical systemSeyyed Alireza Ahmadi0University of Sistan and Baluchestann this paper we associate a pseudo-metric to a dynamical system on a compact metric space. We show that this pseudo-metric is identically zero if and only if the system is chain transitive. If we associate this pseudo-metric to the identity map, then we can present a  characterization for connected and totally disconnected metric spaces.http://polipapers.upv.es/index.php/AGT/article/view/3050chain recurrentchain transitivechain componentinverse limit space.
collection DOAJ
language English
format Article
sources DOAJ
author Seyyed Alireza Ahmadi
spellingShingle Seyyed Alireza Ahmadi
On the topology of the chain recurrent set of a dynamical system
Applied General Topology
chain recurrent
chain transitive
chain component
inverse limit space.
author_facet Seyyed Alireza Ahmadi
author_sort Seyyed Alireza Ahmadi
title On the topology of the chain recurrent set of a dynamical system
title_short On the topology of the chain recurrent set of a dynamical system
title_full On the topology of the chain recurrent set of a dynamical system
title_fullStr On the topology of the chain recurrent set of a dynamical system
title_full_unstemmed On the topology of the chain recurrent set of a dynamical system
title_sort on the topology of the chain recurrent set of a dynamical system
publisher Universitat Politècnica de València
series Applied General Topology
issn 1576-9402
1989-4147
publishDate 2014-06-01
description n this paper we associate a pseudo-metric to a dynamical system on a compact metric space. We show that this pseudo-metric is identically zero if and only if the system is chain transitive. If we associate this pseudo-metric to the identity map, then we can present a  characterization for connected and totally disconnected metric spaces.
topic chain recurrent
chain transitive
chain component
inverse limit space.
url http://polipapers.upv.es/index.php/AGT/article/view/3050
work_keys_str_mv AT seyyedalirezaahmadi onthetopologyofthechainrecurrentsetofadynamicalsystem
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