Topological Ergodicity of Real Cocycles over Minimal Rotations

Abstract.

 We prove that for each minimal rotation on a compact metric group and each topological cocycle , either φ is a topological coboundary, or is topologically ergodic, or the partition into orbits is the decomposition of into minimal components. As an application, we generalize a result by Glasner and show that if is a minimal topologically weakly mixing flow, then whenever φ is universally ergodic the minimal map

is not PI but is disjoint from all minimal topologically weakly mixing systems.