The nonautonomous function-theoretic center problem

We study the linearizability and stability of a nonautonomous dynamical system in the neighborhood of a neutral fixed point. Our results generalize the classical results of Schröder and Siegel in the case when the linear part of the mapping is an irrational rotation, well known results in the rational case and the fundamental result on the representation of the system as a translation in the neighborhood of a fixed point at infinity.