Cocycles with one exponent over partially hyperbolic systems

2011/11/15 by Boris Kalinin, Victoria Sadovskaya, Kalinin, Boris +1 · 3 citations
Mathematics · Physics and Astronomy · #34C20 #37C15 #37D20 #37D30 #37H15 #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1111.3400

openalex publication_date 2011/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Cohomology of GL(2,R)-valued cocycles over hyperbolic systems
• Extremal Lyapunov exponents: an invariance principle and applications
• Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents

Cited by

• Dominated splittings and periodic data for quasi-compact operator cocycles
• On Kanai's conjecture for frame flows over negatively curved manifolds
• Statistical properties of equilibrium states for fiber-bunched matrix cocycles and applications

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