Nonstationary smooth geometric structures for contracting measurable cocycles

Abstract

We implement a differential-geometric approach to normal forms for contracting measurable cocycles to $\mbox{Diff}^q({\bf R}^n, {\bf 0})$, $q\ge 2$. 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.

various corrections made and remarks added; 38 pp; to appear in revised form subject to editorial input in Ergodic Theory and Dynamical Systems (see DOI)

References in corpus (2)

• Global rigidity for totally nonsymplectic Anosov Z^k actions
• On Hoelder-continuity of Oseledets subspaces