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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 281395, 6 pages
http://dx.doi.org/10.1155/2013/281395
Research Article

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

Department of Mathematics, Shangqiu Normal University, Shangqiu, Henan 476000, China

Received 3 March 2013; Accepted 15 May 2013

Academic Editor: Carlo Piccardi

Copyright © 2013 Lei Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.