Cocycles with one exponent over partially hyperbolic systems

Boris Kalinin; Victoria Sadovskaya

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arXiv · 1111.3400

Cocycles with one exponent over partially hyperbolic systems

Boris Kalinin·Victoria Sadovskaya

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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.

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Boris Kalinin, Victoria Sadovskaya. 2011-11-15. Cocycles with one exponent over partially hyperbolic systems. https://arxiv.org/abs/1111.3400

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