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arXiv · 1803.06402

Shadowing for nonautonomous dynamics

Lucas Backes·Davor Dragicevic
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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.

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Lucas Backes, Davor Dragicevic. 2018-03-16. Shadowing for nonautonomous dynamics. https://doi.org/10.1515/ans-2018-2033

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