Center manifolds depending on a parameter

For differential equations u′=A(t)u+f(t,u,λ)u′=A(t)u+f(t,u,λ) obtained from sufficiently small C1C1 perturbations of a nonuniform exponential trichotomy, we establish the C1C1 dependence of the center manifolds on the parameter λλ. Our proof uses the fiber contraction principle to establish the regularity property. We note that our argument also applies to linear perturbations, without further changes.