Some remarks on chaos in topological dynamics


  • Huoyung Wang Guangzhou University
  • Heman Fu Zhaoqing University



Sensitivity, Chaos, Tree maps


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


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How to Cite

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



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