Normal Forms for Nonautonomous Nonlinear Difference Systems Under Nonuniform Dichotomy Spectrum

Abstract

In this paper, the normal forms of nonautonomous nonlinear systems with discrete time are investigated. We first employ the nonuniform kinematic similarity to prove the nonuniform dichotomy spectrum theorem, which is not based on linear integral manifolds in most of the previous works. Using this spectral theorem, we extend smooth normal forms from autonomous difference systems to nonautonomous ones.