Holonomies and cohomology for cocycles over partially hyperbolic diffeomorphisms

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We consider group-valued cocycles over a partially hyperbolic dif-feomorphism 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 continuous conjugacy between two cocycles.

Original languageEnglish (US)
Pages (from-to)245-259
Number of pages15
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number1
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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