Degree, mixing, and absolutely continuous spectrum of cocycles with values in compact Lie groups

Rafael Tiedra de Aldecoa

We consider skew products $$T_{\varphi }:X\times G\to X\times G,(x,g)\mapsto (F_1(x),g\varphi (x)),$$ where $X$ is a compact manifold with probability measure, $G$ a compact Lie group with Li…