Stable ergodicity of skew products

Abstract

Stable ergodicity is dense among compact Lie group extensions of Anosov diffeomorphisms of compact manifolds. Under the additional assumption that the base map acts on an infranilmanifold, an extension that is not stably ergodic must have a factor that has one of three special forms. A consequence is that stable ergodicity and stable ergodicity within skew products are equivalent in this case.