About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 583431, 4 pages
http://dx.doi.org/10.1155/2014/583431
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.

Linked References

  1. D. Ruelle and F. Takens, “On the nature of turbulence,” Communications in Mathematical Physics, vol. 20, pp. 167–192, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. D. Ruelle and F. Takens, “Note concerning our paper: “On the nature of turbulence”,” Communications in Mathematical Physics, vol. 23, pp. 343–344, 1971.
  3. J. Auslander and J. A. Yorke, “Interval maps, factors of maps, and chaos,” The Tôhoku Mathematical Journal, vol. 32, no. 2, pp. 177–188, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. Devaney, Chaotic Dynamical Systems, Addison-Wesley, Reading, Mass, USA, 1989.
  5. G. F. Liao, L. D. Wang, and Y. C. Zhang, “Transitivity, mixing and chaos for a class of set-valued mappings,” Science in China A: Mathematics, vol. 49, no. 1, pp. 1–8, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. E. Glasner and B. Weiss, “Sensitive dependence on initial conditions,” Nonlinearity, vol. 6, no. 6, pp. 1067–1075, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. E. Akin and S. Kolyada, “Li-Yorke sensitivity,” Nonlinearity, vol. 16, no. 4, pp. 1421–1433, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  8. H. Wang, X. Long, and H. Fu, “Sensitivity and chaos of semigroup actions,” Semigroup Forum, vol. 84, no. 1, pp. 81–90, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Glasner and D. Maon, “Rigidity in topological dynamics,” Ergodic Theory and Dynamical Systems, vol. 9, no. 2, pp. 309–320, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W. Huang and X. Ye, “An explicit scattering, non-weakly mixing example and weak disjointness,” Nonlinearity, vol. 15, no. 3, pp. 849–862, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. K. S. Moothathu, “Stronger forms of sensitivity for dynamical systems,” Nonlinearity, vol. 20, no. 9, pp. 2115–2126, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. Y. Wang, J. C. Xiong, and F. Tan, “Furstenberg families and sensitivity,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 649348, 12 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. H. Liu, E. Shi, and G. Liao, “Sensitivity of set-valued discrete systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 12, pp. 6122–6125, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. P. Sharma and A. Nagar, “Inducing sensitivity on hyperspaces,” Topology and its Applications, vol. 157, no. 13, pp. 2052–2058, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. X. Ye and R. Zhang, “On sensitive sets in topological dynamics,” Nonlinearity, vol. 21, no. 7, pp. 1601–1620, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet