Sensitivity of the Product System of Set-Valued Non-Autonomous Discrete Dynamical Systems

Yongxi Jiang,Jingmin Pi,Xiaofang Yang,Tianxiu Lu

doi:10.4236/jamp.2021.911174

Abstract

This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between or and the product system in sensitivity, infinite sensitivity, F-sensitivity, (F1, F2)-sensitivity. Then, the relation between (X, f1,∞) or (Y, g1,∞) and in ergodic sensitivity is obtained. Where is the set-valued dynamical system induced by a non-autonomous discrete dynamical system (X, f1,∞).

Highlights

Since the beginning of the 21st century, the problem of chaos in set-valued discrete systems has been discussed warmly
Many scholars studied the chaotic properties of set-valued discrete systems
In 2013, they gave an example to show that Li-Yorke sensitivity of f does not necessarily imply Li-Yorke sensitivity of f ([11])

Summary

Introduction

Since the beginning of the 21st century, the problem of chaos in set-valued discrete systems has been discussed warmly. Many scholars studied the chaotic properties of set-valued discrete systems. In 2013, they gave an example to show that Li-Yorke sensitivity of f does not necessarily imply Li-Yorke sensitivity of f ([11]). Inspired by the literature [13]-[17], this paper further studies some stronger forms of sensitivity in set-valued discrete systems.

Non-Autonomous Discrete System

Set-Valued Product Systems

Definitions of Sensitivity

Main Results

Conclusion