Abstract
We consider Hölder 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 the quasiconformal distortion from the periodic data.
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Boris Kalinin and Victoria Sadovskaya are Supported in part by NSF grant DMS-1101150 and NSF grant DMS-0901842 respectively.
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Kalinin, B., Sadovskaya, V. Cocycles with one exponent over partially hyperbolic systems. Geom Dedicata 167, 167–188 (2013). https://doi.org/10.1007/s10711-012-9808-z
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DOI: https://doi.org/10.1007/s10711-012-9808-z