Generic linear cocycles over a minimal base

TL;DR

This paper proves that generically, linear cocycles over minimal base dynamics exhibit a finest dominated splitting that aligns with the Oseledets splitting, extending previous results to higher dimensions.

Contribution

It extends the understanding of linear cocycles by showing generic properties of their splittings over minimal systems in finite dimensions.

Findings

Oseledets splitting coincides with the finest dominated splitting almost everywhere.

Restriction to subbundles is uniformly subexponentially quasiconformal.

Generalizes previous SL(2,R) results to higher dimensions.

Abstract

We prove 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. This extends a previous result for SL(2,R)-cocycles due to Avila and the author.