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arXiv · 1408.5602

Holonomies and cohomology for cocycles over partially hyperbolic diffeomorphisms

Boris Kalinin·Victoria Sadovskaya
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Abstract

We consider group-valued cocycles over a partially hyperbolic diffeomorphism which is accessible volume-preserving and center bunched. We study cocycles with values in the group of invertible continuous linear operators on a Banach space. We describe properties of holonomies for fiber bunched cocycles and establish their Holder regularity. We also study cohomology of cocycles and its connection with holonomies. We obtain a result on regularity of a measurable conjugacy, as well as a necessary and sufficient condition for existence of a contionuous conjugacy between two cocycles.

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Boris Kalinin, Victoria Sadovskaya. 2014-08-24. Holonomies and cohomology for cocycles over partially hyperbolic diffeomorphisms. https://arxiv.org/abs/1408.5602

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