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Non-stationary smooth geometric structures for contracting measurable cocycles
Published online by Cambridge University Press: 28 June 2017
Abstract
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We implement a differential-geometric approach to normal forms for contracting measurable cocycles to 
$\operatorname{Diff}^{q}(\mathbb{R}^{n},\mathbf{0})$, 
$q\geq 2$. We obtain resonance polynomial normal forms for the contracting cocycle and its centralizer, via 
$C^{q}$ changes of coordinates. These are interpreted as non-stationary 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.
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