Cohomology of GL(2,R)-valued cocycles over hyperbolic systems

2010/08/16 by Victoria Sadovskaya, Sadovskaya, Victoria · 3 citations
Mathematics · #37D20 #37H15 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1008.2564

openalex publication_date 2010/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Holder continuous GL(2,R)-valued cocycles over a transitive Anosov diffeomorphism. We give a complete classification up to Holder cohomology of cocycles with one Lyapunov exponent and of cocycles that preserve two transverse Holder continuous sub-bundles. We prove that a measurable cohomology between two such cocycles is Holder continuous. We also show that conjugacy of periodic data for two such cocycles does not always imply cohomology, but a slightly stronger assumption does. We describe examples that indicate that our main results do not extend to general GL(2,R)-valued cocycles.

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• Cocycles with one exponent over partially hyperbolic systems
• Lyapunov non-typical behavior for linear cocycles through the lens of semigroup actions
• Fiber bunching and cohomology for Banach cocycles over hyperbolic\n systems

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