Author(s)

Xiaofang Yang¹, Yongxi Jiang¹, Tianxiu Lu^1,2*

¹College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, China.
²Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong, China.

Let be a non-autonomous discrete system and  be a set-valued discrete system induced by it. Where, is the space formed by all non-empty compact subsets of X endowed with the Hausdorff metric H, is a set-valued mapping sequence induced by . It is proved that  is -chaos, then  is -chaos. Where -chaos is denoted to -sensitive, -sensitive, -transitive, -accessible, -weakly mixing, -m-sensitive, infinitely sensitive, or syndetically transitive.

Furstenberg Family, Non-Autonomous Discrete System, F -Sensitive, F -Transitive, F -Accessible, F -Weakly Mixing, F -m-Sensitive

Yang, X. , Jiang, Y. and Lu, T. (2021) Chaotic Properties in the Sense of Furstenberg Families in Set-Valued Discrete Dynamical Systems. Open Journal of Applied Sciences, 11, 343-353. doi: 10.4236/ojapps.2021.113025.