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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 260856, 5 pages
http://dx.doi.org/10.1155/2013/260856
Research Article

Li-Yorke Sensitivity of Set-Valued Discrete Systems

1Department of Mathematics, Dalian University of Technology, Dalian, Liaoning 116600, China
2Department of Mathematics, Dalian Nationalities University, Dalian, Liaoning 116600, China

Received 6 October 2013; Accepted 27 November 2013

Academic Editor: Hongya Gao

Copyright © 2013 Heng Liu et al. 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

Consider the surjective, continuous map and the continuous map of induced by , where is a compact metric space and is the space of all nonempty compact subsets of endowed with the Hausdorff metric. In this paper, we give a short proof that if is Li-Yoke sensitive, then is Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity of does not imply Li-Yorke sensitivity of .