engleski

Shadowing for nonautonomous dynamics

We prove that whenever a sequence of invertible and bounded operators (Am)m∈Z acting on a Banach space X admits an exponential dichotomy and a sequence of differentiable maps fm : X → X, m ∈ Z, has bounded and H¨older derivatives, the nonautonomous dynamics given by xm+1 = Amxm + fm(xm), m ∈ Z has various shadowing properties. Hence, we extend recent results of Bernardes Jr. et al. in several directions. As a nontrivial application of our results, we give a new proof of the nonautonomous Grobman- Hartman theorem.

Shadowing, Nonautonomus systems, Exponential dichotomies, Nonlinear perturbations.

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