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arXiv · 1612.03453

Fiber bunching and cohomology for Banach cocycles over hyperbolic systems

Victoria Sadovskaya
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Abstract

We consider Holder 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 Holder continuously cohomologous if and only if they have Holder 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 Holder continuity of a measurable conjugacy between a fiber bunched cocycle and one with values in a set which is compact in strong operator topology.

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Victoria Sadovskaya. 2016-12-11. Fiber bunching and cohomology for Banach cocycles over hyperbolic systems. https://arxiv.org/abs/1612.03453

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