Cocycles with one exponent over partially hyperbolic systems

Details Cocycles with one exponent over partially hyperbolic systems Cocycles with one exponent over partially hyperbolic systems

2011-11-15

arxiv.org/abs/1111.3400v1

Mathematics

Dynamical Systems

17 pages

Scientific paper

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.

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