On the Eventual Shadowing Property and Eventually Shadowable Point of Set-valued Dynamical Systems  

作　　者：Xue Rong XIE Jian Dong YIN 

机构地区：[1]Department of Mathematics,Nanchang University,Nanchang 330031,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第6期1105-1115,共11页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.12061043,11661054,11261039)。

摘　　要：The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a set-valued dynamical system has the eventual shadowing property if and only if every point in the phase space is eventually shadowable;every chain transitive set-valued dynamical system has either the eventual shadowing property or no eventually shadowable points;and a set-valued dynamical system admits an eventually shadowable point if and only if it admits a minimal eventually shadowable point.Moreover,it is proved that a set-valued dynamical system with the eventual shadowing property is chain mixing if and only if it is mixing and if and only if it has the specification property.

关 键 词：Eventual shadowing property eventually shadowable point set-valued dynamical system SPECIFICATION 

分 类 号：O19[理学—数学]