The Retentivity of Four Kinds of Shadowing Properties in Non-Autonomous Discrete Dynamical Systems

Abstract

In this paper, four kinds of shadowing properties in non-autonomous discrete dynamical systems (NDDSs) are discussed. It is pointed out that if an NDDS has a F-shadowing property (resp. ergodic shadowing property, d¯ shadowing property, d̲ shadowing property), then the compound systems, conjugate systems, and product systems all have accordant shadowing properties. Moreover, the set-valued system (K(X),f¯1,∞) induced by the NDDS (X,f1,∞) has the above four shadowing properties, implying that the NDDS (X,f1,∞) has these properties.

Keywords

• shadowing properties
• non-autonomous discrete dynamical systems
• set-valued systems