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Cocycles with one exponent over partially hyperbolic systems (1111.3400v2)
Published 15 Nov 2011 in math.DS
Abstract: We consider Holder continuous linear cocycles over partially hyperbolic diffeomorphisms. For fiber bunched cocycles with one Lyapunov exponent we show continuity of measurable invariant conformal structures and sub-bundles. Further, we establish a continuous version of Zimmer's Amenable Reduction Theorem. For cocycles over hyperbolic systems we also obtain polynomial growth estimates for the norm and quasiconformal distortion from the periodic data.