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arXiv · 1710.06662

Smooth Linearization of Nonautonomous Difference Equations with a Nonuniform Dichotomy

Davor Dragicevic·Weinian Zhang·Wenmeng Zhang
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Abstract

In this paper we give a smooth linearization theorem for nonautonomous difference equations with a nonuniform strong exponential dichotomy. The linear part of such a nonautonomous difference equation is defined by a sequence of invertible linear operators on $\mathbb{R}^d$. Reducing the linear part to a bounded linear operator on a Banach space, we discuss the spectrum and its spectral gaps. Then we obtain a gap condition for $C^1$ linearization of such a nonautonomous difference equation. We finally extend the result to the infinite dimensional case. Our theorems improve known results even in the case of uniform strong exponential dichotomies.

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Davor Dragicevic, Weinian Zhang, Wenmeng Zhang. 2019-07-07. Smooth Linearization of Nonautonomous Difference Equations with a Nonuniform Dichotomy. https://arxiv.org/abs/1710.06662

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