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 language||English (US)|
|Number of pages||14|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|State||Published - Sep 2017|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics