Affiliation:
1. School of Mathematic and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
2. College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
3. South Sichuan Applied Mathematics Research Center, Zigong 643000, China
Abstract
Assume that (Y,ρ) is a nontrivial complete metric space, and that (Y,g1,∞) is a time-varying discrete dynamical system (T-VDDS), which is given by sequences (gl)l=1∞ of continuous selfmaps gl:Y→Y. In this paper, for a given Furstenberg family G and a given T-VDDS (Y,g1,∞), G-scrambled pairs of points of the system (Y,g1,∞) (which contains the well-known scrambled pairs) are provided. Some properties of the set of G-scrambled pairs of a given T-VDDS (Y,g1,∞) are studied. Moreover, the generically G-chaotic T-VDDS and the generically strongly G-chaotic T-VDDS are defined. A sufficient condition for a given T-VDDS to be generically strongly G-chaotic is also presented.
Funder
Natural Science Foundation of Sichuan Province
Opening Project of Artificial Intelligence Key Laboratory of Sichuan Province
Key Scientific and Technological Research Project of Science and Technology Department of Zhanjiang City
Scientific Research Project of SUSE