On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems

On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems

Blanchard and Huang introduced the notion of weakly mixing subset, and Oprocha and Zhang gave the concept of transitive subset and studied its basic properties. In this paper our main goal is to discuss the weakly mixing subsets and transitive subsets in set-valued discrete systems. We prove that a...

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Main Author: Lei Liu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2013/281395
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spelling doaj-b70221efb96d4b959d7b475f7d5756e52020-11-24T23:51:15ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/281395281395On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete SystemsLei Liu0Department of Mathematics, Shangqiu Normal University, Shangqiu, Henan 476000, ChinaBlanchard and Huang introduced the notion of weakly mixing subset, and Oprocha and Zhang gave the concept of transitive subset and studied its basic properties. In this paper our main goal is to discuss the weakly mixing subsets and transitive subsets in set-valued discrete systems. We prove that a set-valued discrete system has a transitive subset if and only if original system has a weakly mixing subset. Moreover, we give an example showing that original system has a transitive subset, which does not imply set-valued discrete system has a transitive subset.http://dx.doi.org/10.1155/2013/281395
collection DOAJ
language English
format Article
sources DOAJ
author Lei Liu
spellingShingle Lei Liu
On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems
Discrete Dynamics in Nature and Society
author_facet Lei Liu
author_sort Lei Liu
title On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems
title_short On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems
title_full On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems
title_fullStr On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems
title_full_unstemmed On Local Aspects of Topological Transitivity and Weak Mixing in Set-Valued Discrete Systems
title_sort on local aspects of topological transitivity and weak mixing in set-valued discrete systems
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2013-01-01
description Blanchard and Huang introduced the notion of weakly mixing subset, and Oprocha and Zhang gave the concept of transitive subset and studied its basic properties. In this paper our main goal is to discuss the weakly mixing subsets and transitive subsets in set-valued discrete systems. We prove that a set-valued discrete system has a transitive subset if and only if original system has a weakly mixing subset. Moreover, we give an example showing that original system has a transitive subset, which does not imply set-valued discrete system has a transitive subset.
url http://dx.doi.org/10.1155/2013/281395
work_keys_str_mv AT leiliu onlocalaspectsoftopologicaltransitivityandweakmixinginsetvalueddiscretesystems
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