engleski

Smooth Linearization of Nonautonomous Difference Equations with a Nonuniform Dichotomy

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 Rd. 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 C1 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.

nonautonomous difference equation ; nonuniform strong exponential dichotomy ; smooth linearization ; spectral gap.

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