Normal forms for contracting measurable cocycles

The history of normal forms theorems for contracting diffeomorphisms of R^n (fixing the origin) includes work of Poincaré, Hartman + Grobman, and Sternberg.  More recently, Guysinsky and Katok proved existence of nonstationary polynomial normal forms, for families of such diffeomorphisms arising from an action on an R^n-bundle.  I will discuss these normal forms results and present work in progress on such a result for contracting measurable cocycles, as well as an interpretation in terms of differential-geometric structures.