Cocycles with one exponent over partially hyperbolic systems

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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.

Original languageEnglish (US)
Pages (from-to)167-188
Number of pages22
JournalGeometriae Dedicata
Volume167
Issue number1
DOIs
StatePublished - Dec 1 2013

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All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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