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Non-stationary smooth geometric structures for contracting measurable cocycles

Published online by Cambridge University Press:  28 June 2017

KARIN MELNICK
KARIN MELNICK*
Affiliation:
Department of Mathematics, 4176 Campus Drive, University of Maryland, College Park, MD 20742, USA email karin@math.umd.edu
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Abstract

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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Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 2 , February 2019 , pp. 392 - 424
Copyright
© Cambridge University Press, 2017 

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