Holonomies and cohomology for cocycles over partially hyperbolic\n diffeomorphisms

2014/08/24 by Boris Kalinin, Victoria Sadovskaya, Kalinin, Boris +1
Mathematics · Physics and Astronomy · #37C15 #37D30 #37H05 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1408.5602

openalex publication_date 2014/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider group-valued cocycles over a partially hyperbolic diffeomorphism\nwhich is accessible volume-preserving and center bunched. We study cocycles\nwith values in the group of invertible continuous linear operators on a Banach\nspace. We describe properties of holonomies for fiber bunched cocycles and\nestablish their Holder regularity. We also study cohomology of cocycles and its\nconnection with holonomies. We obtain a result on regularity of a measurable\nconjugacy, as well as a necessary and sufficient condition for existence of a\ncontionuous conjugacy between two cocycles.\n

Citations

• Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents

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