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Non-stationary smooth geometric structures for contracting measurable cocycles

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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… Click to show full 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.

Keywords: stationary smooth; geometric structures; non stationary; measurable cocycles; contracting measurable; smooth geometric

Journal Title: Ergodic Theory and Dynamical Systems
Year Published: 2017

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