Cocycles with one exponent over partially hyperbolic systems

By B. Kalinin, V. Sadovskaya. 2011

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/09e0e7826b718cd66d2fefb4cf041aeac786a17f