Chaos for finitely generated semigroup actions

Volume 10, Issue 7, pp 3843--3850 http://dx.doi.org/10.22436/jnsa.010.07.38

Publication Date: July 27, 2017 Submission Date: May 18, 2016

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Authors

Lidong Wang - School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China. - Department of Mathematics, Dalian Minzu University, Dalian, 116600, People’s Republic of China. Yingcui Zhao - School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China. Zhenyan Chu - Department of Mathematics, Dalian Minzu University, Dalian, 116600, People’s Republic of China.

Abstract

In this paper, we define and study Li-Yorke chaos and distributional chaos along a sequence for finitely generated semigroup actions. Let X be a compact space with metric d and G be a semigroup generated by \(f_1, f_2, ..., f_m\) which are finitely many continuous mappings from X to itself. Then we show if (X,G) is transitive and there exists a common fixed point for all the above mappings, then (X,G) is chaotic in the sense of Li-Yorke. And we give a sufficient condition for (X,G) to be uniformly distributionally chaotic along a sequence and chaotic in the strong sense of Li-Yorke. At the end of this paper, an example on the one-sided symbolic dynamical system for (X,G) to be chaotic in the strong sense of Li-Yorke and uniformly distributionally chaotic along a sequence is given.

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ISRP Style

Lidong Wang, Yingcui Zhao, Zhenyan Chu, Chaos for finitely generated semigroup actions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3843--3850

AMA Style

Wang Lidong, Zhao Yingcui, Chu Zhenyan, Chaos for finitely generated semigroup actions. J. Nonlinear Sci. Appl. (2017); 10(7):3843--3850

Chicago/Turabian Style

Wang, Lidong, Zhao, Yingcui, Chu, Zhenyan. "Chaos for finitely generated semigroup actions." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3843--3850

Keywords

Li-Yorke chaos
distributional chaos along a sequence
finitely generated semigroup actions.

MSC

54H20
22B99
37B05

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