  We implement a differential-geometric approach to normal forms for
contracting measurable cocycles to $\mbox{Diff}^q({\bf R}^n, {\bf 0})$, $q \geq
2$. We obtain resonance polynomial normal forms for the contracting cocycle and
its centralizer, via $C^q$ changes of coordinates. These are interpreted as
nonstationary invariant differential-geometric structures. We also consider the
case of contracted foliations in a manifold, and obtain $C^q$ homogeneous
structures on leaves for an action of the group of subresonance polynomial
diffeomorphisms together with translations.
