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

Volume 20, Issue 1, pp 14--20 http://dx.doi.org/10.22436/jmcs.020.01.02
Publication Date: August 20, 2019 Submission Date: December 14, 2018 Revision Date: July 13, 2019 Accteptance Date: July 23, 2019

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.


Keywords


MSC


References