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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 583431, 4 pages
Research Article

Thickly Syndetical Sensitivity of Topological Dynamical System

1Department of Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, China
2Department of Mathematics, Dalian Nationalities University, Dalian, Liaoning 116600, China
3Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Received 7 January 2014; Accepted 1 April 2014; Published 24 April 2014

Academic Editor: Mingshu Peng

Copyright © 2014 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.


Consider the surjective continuous map , where is a compact metric space. In this paper we give several stronger versions of sensitivity, such as thick sensitivity, syndetic sensitivity, thickly syndetic sensitivity, and strong sensitivity. We establish the following. (1) If is minimal and sensitive, then is syndetically sensitive. (2) Weak mixing implies thick sensitivity. (3) If is minimal and weakly mixing, then it is thickly syndetically sensitive. (4) If is a nonminimal -system, then it is thickly syndetically sensitive. Devaney chaos implies thickly periodic sensitivity. (5) We give a syndetically sensitive system which is not thickly sensitive. (6) We give thickly syndetically sensitive examples but not cofinitely sensitive ones.