The Shadowing Properties Of Nonautonomous Dynamical System

Let (Xₙ, dₙ) be a sequence of metric spaces and let F=ₙ ∈ Z be a sequence of continuous and onto maps fₙ: Xₙ → Xₙ₊₁, n ∈ Z₊. In this paper, we prove that if the compression ratio meets ∏ λᵢ=0, then there exists δₙ>0 such that any δₙ - pseudo-orbit ₙ ∈ Z is ε - shadowed by a unique point x ∈ X₀. For the asymptotic average shadowing property, we prove that if .F|A has asymptotically average shadowing property, then F also has a asymptotically average shadowing propertywhen a density-related condition is satisfied. Additionally, the conclusion that the shadowing performance of strong equicontinuity and pseudo-shadowing property implies limit shadowing is also obtained. Furthermore, the shadowing property of non-autonomous product space is also discussed.