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

作　　者：Xiao Fang LUO Xiao Xiao NIE 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》2020年第12期1384-1394,共11页数学学报（英文版）

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

摘　　要：In this article,the authors introduce the concept of shadowable points for set-valued dynamical systems,the pointwise version of the shadowing property,and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable;every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points;and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable point.In the end,it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property.

关 键 词：Shadowing property shadowable point set-valued dynamical system SPECIFICATION 

分 类 号：O19[理学—数学]