Generic linear cocycles over a minimal base (Q2856676)

The author proves that a generic linear cocycle over a minimal base dynamics of finite dimension has the property that the Oseledets splitting with respect to any invariant probability coincides almost everywhere with the finest dominated splitting. Therefore the restriction of the generic cocycle to a subbundle of the finest dominated splitting is uniformly subexponentially quasiconformal.NEWLINENEWLINEThis work extends a previous result due to \textit{A. Avila} and \textit{J. Bochi} [Bull. Soc. Math. Fr. 135, No. 3, 407--417 (2007; Zbl 1217.37017)]. In the proof, the author introduces an especially convenient semicontinuous function \(Z\) to measure the quasiconformal distortion in order to deal simultaneously with several Lyapunov exponents with respect to all invariant measures.