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

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

2010-08-16

arxiv.org/abs/1008.2564v2

Mathematics

Dynamical Systems

Scientific paper

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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