Cohomology of Dominated Diffeomorphism-Valued Cocycles Over Hyperbolic Systems

Abstract

We prove a rigidity theorem for dominated Hölder cocycles with values on diffeomorphism groups of a compact manifold over hyperbolic homeomorphisms. More precisely, we show that if two such cocycles have equal periodic data, then they are cohomologous.

A few improvements were made. To appear in Ergod. Th. & Dynam. Syst