# American Institute of Mathematical Sciences

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January  2016, 36(1): 245-259. doi: 10.3934/dcds.2016.36.245

## Holonomies and cohomology for cocycles over partially hyperbolic diffeomorphisms

 1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States

Received  August 2014 Revised  February 2015 Published  June 2015

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 Hölder 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 continuous conjugacy between two cocycles.
Citation: Boris Kalinin, Victoria Sadovskaya. Holonomies and cohomology for cocycles over partially hyperbolic diffeomorphisms. Discrete & Continuous Dynamical Systems, 2016, 36 (1) : 245-259. doi: 10.3934/dcds.2016.36.245
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