  The main purpose of this paper is to formulate new conditions for smooth
linearization of nonautonomous systems with discrete and continuous time. Our
results assume that the linear part admits a nonuniform polynomial dichotomy
and that the associated polynomial dichotomy spectrum exhibits appropriate
spectral gap and spectral band conditions. This is in sharp contrast to most of
the previous results in the literature which assumed that the linear part
admits an exponential dichotomy. Our techniques exploit the relationship
between polynomial and exponential dichotomies via a suitable reparametrization
of time.
