Fiber bunching and cohomology for banach cocycles over hyperbolic systems

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Abstract

We consider Hölder continuous cocycles over hyperbolic dynamical systems with values in the group of invertible bounded linear operators on a Banach space. We show that two fiber bunched cocycles are Hölder continuously cohomologous if and only if they have Hölder conjugate periodic data. The fiber bunching condition means that non-conformality of the cocycle is dominated by the expansion and contraction in the base system. We show that this condition can be established based on the periodic data of a cocycle. We also establish Hölder continuity of a measurable conjugacy between a fiber bunched cocycle and one with values in a set which is compact in strong operator topology.

Original languageEnglish (US)
Pages (from-to)4959-4972
Number of pages14
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume37
Issue number9
DOIs
StatePublished - Sep 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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