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

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) over bar shadowing property, (d) under bar shadowing property), then the compound systems, conjugate systems, and product systems all have accordant shadowing properties. Moreover, the set-valued system (K(X), (f) over bar (1,infinity)) induced by the NDDS (X, f(1,)(infinity)) has the above four shadowing properties, implying that the NDDS (X, f(1,infinity)) has these properties.