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

• 作者: Jian Dong YIN Xiao Fang LUO Xiao Xiao NIE
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2020,（12）
• 页码范围: 1384-1394
• 页数: 11页
• 语种: 英文

摘要

In this article, the authors introduce the concept of shadowable points for set-valued dy-namical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iffevery point in the phase space is shadowable;every chain tran-sitive 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.