# Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems

Volume 20, Issue 1, pp 14--20
Publication Date: August 20, 2019 Submission Date: December 14, 2018 Revision Date: July 13, 2019 Accteptance Date: July 23, 2019
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### Authors

Yu Zhao - School of Mathematics and Computer Science , Guangdong Ocean University, Zhanjiang, 524025, P. R. China. Risong Li - School of Mathematics and Computer Science , Guangdong Ocean University, Zhanjiang, 524025, P. R. China. Hongqing Wang - School of Mathematics and Computer Science , Guangdong Ocean University, Zhanjiang, 524025, P. R. China. Haihua Liang - School of Mathematics and Computer Science , Guangdong Ocean University, Zhanjiang, 524025, P. R. China.

### Abstract

Assume that $(W, g_{1,\infty})$ is a nonautonomous discrete dynamical system given by sequences $(g_{m})_{m=1}^{\infty}$ of continuous maps on the space $(W,d)$. In this paper, it is proven that if $g_{1, \infty}$ is topologically weakly mixing and satisfies that $g_{1}^{n}\circ g_{1}^{m}=g_{1}^{n+m}$ for any $n,m\in\{0,1,\ldots\}$, then it is distributional chaos in a sequence. This result extends the existing one.

### Share and Cite

##### ISRP Style

Yu Zhao, Risong Li, Hongqing Wang, Haihua Liang, Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems, Journal of Mathematics and Computer Science, 20 (2020), no. 1, 14--20

##### AMA Style

Zhao Yu, Li Risong, Wang Hongqing, Liang Haihua, Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems. J Math Comput SCI-JM. (2020); 20(1):14--20

##### Chicago/Turabian Style

Zhao, Yu, Li, Risong, Wang, Hongqing, Liang, Haihua. "Distributional chaos in a sequence and topologically weak mixing for nonautonomous discrete dynamical systems." Journal of Mathematics and Computer Science, 20, no. 1 (2020): 14--20

### Keywords

• Chaotic in the sense of Devaney
• topologically transitive
• sensitive
• nonautonomous discrete dynamical systems
• distributional chaos in a sequence

•  54H20
•  37B40
•  37D45

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