  Takens Theorem for a partially hyperbolic dynamics provides a normal
linearization along the center manifold. In this paper, we give the
nonautonomous version of Takens Theorem under non-resonance conditions
formulated in terms of the dichotomy spectrum. In our proof, one difficulty is
to solve homological equations for the normal form theory which involve a
center variable, while another difficulty is to find the dichotomy spectrum of
a certain matrix cocycle that is block lower triangular. In order to overcome
those difficulties, in comparison with the autonomous case, we need an
additional term in the (nonautonomous) non-resonance conditions to guarantee
certain spectral gap conditions. This additional term disappears naturally in
the autonomous case.
