Cohomology of Lipschitz-valued cocycles

Abstract

We consider the set of Hölder continuous cocycles over a finite shift acting on a group of Lipschitz homeomorphisms Lip(G), where G is a metrisable compact topological group. We establish that two dominated cocycles that coincide over periodic points of the base are cohomologous, with the conjugacy being Hölder continuous. Moreover, we prove that, under an additional condition, the existence of a measurable conjugacy implies the existence of a Hölder continuous conjugacy between the cocycles.