Topological Wiener–Wintner ergodic theorems via non-abelian Lie group extensions

Abstract

AbstractWe generalize a series of topological Wiener–Wintner ergodic theorems due to Walters to the context of group extensions of measure-preserving transformations where the group is a non-abelian compact Lie group. Applications to random ergodic theorems for a shift map are given.