Some remarks on chaos in topological dynamics

Authors

  • Huoyung Wang Guangzhou University
  • Heman Fu Zhaoqing University

DOI:

https://doi.org/10.4995/agt.2011.1645

Keywords:

Sensitivity, Chaos, Tree maps

Abstract

Bau-Sen Du introduced a notion of chaos which is stronger than Li-Yorke sensitivity. A TDS (X, f) is called chaotic if there is a positive e such that for any x and any nonempty open set V of X there is a point y in V such that the pair (x, y) is proximal but not e-asymptotic. In this article, we show that a TDS (T, f) is transitive but not mixing if and only if (T, f) is Li-Yorke sensitive but not chaotic, where T is a tree. Moreover, we compare such chaos with other notions of chaos.

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Author Biographies

Huoyung Wang, Guangzhou University

Department of Mathematics, Guangzhou University, Guangzhou, 510006, People's Republic of China

Heman Fu, Zhaoqing University

College of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, 526061, People's Republic of China

References

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B. Du, On the nature of chaos, arXiv: math.DS/0602585 v1 26 Feb 2006.

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X. Ye, W. Huang and S. Shao, An Introduction to Topolgical Dynamics, Science Press, Bejing, 2008. [Chinese]

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How to Cite

[1]
H. Wang and H. Fu, “Some remarks on chaos in topological dynamics”, Appl. Gen. Topol., vol. 12, no. 2, pp. 95–100, Oct. 2011.

Issue

Section

Regular Articles