math.DS

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# Title: Shadowing for nonautonomous dynamics

Abstract: We prove that whenever a sequence of invertible and bounded operators $(A_m)_{m\in \mathbb{Z}}$ acting on a Banach space $X$ admits an exponential dichotomy and a sequence of differentiable maps $f_m \colon X\to X$, $m\in \mathbb{Z}$, has bounded and H\"{o}lder derivatives, the nonautonomous dynamics given by $x_{m+1}=A_mx_m+f_m(x_m)$, $m\in \mathbb{Z}$ 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.
 Subjects: Dynamical Systems (math.DS) Cite as: arXiv:1803.06402 [math.DS] (or arXiv:1803.06402v1 [math.DS] for this version)

## Submission history

From: Lucas Backes [view email]
[v1] Fri, 16 Mar 2018 21:15:43 GMT (13kb)