Center manifolds for difference equations-smooth parameter dependence (Q984045)

The authors prove the existence of \(C^{1}\) center manifolds for a class of difference equations of the form \(v_{m+1}=A_{m}v_{m}+f_{m}(v_{m},\lambda)\). They also prove that these center manifolds are also \(C^{1}\) on the parameter \(\lambda\). The class of difference equations is determined by the notion of ``nonuniform exponential trichotomy''.