Cohomology of GL(2,R)-valued cocycles over hyperbolic systems
Dynamical Systems
2011-04-19 v2
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.
Keywords
Cite
@article{arxiv.1008.2564,
title = {Cohomology of GL(2,R)-valued cocycles over hyperbolic systems},
author = {Victoria Sadovskaya},
journal= {arXiv preprint arXiv:1008.2564},
year = {2011}
}