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Non-stationary smooth geometric structures for contracting measurable cocycles

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Melnick,  Karin
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Melnick, K. (2019). Non-stationary smooth geometric structures for contracting measurable cocycles. Ergodic Theory and Dynamical Systems, 39(2), 392-424. doi:10.1017/etds.2017.38.


Cite as: https://hdl.handle.net/21.11116/0000-0004-6766-6
Abstract
We implement a differential-geometric approach to normal forms for contracting measurable cocycles to $\mbox{Diff}^q({\bf R}^n, {\bf 0})$, $q \geq2$. 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.