Generic linear cocycles over a minimal base
Volume 218 / 2013
Studia Mathematica 218 (2013), 167-188
MSC: Primary 37H15.
DOI: 10.4064/sm218-2-4
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 $\mathrm {SL}(2,\mathbb {R})$-cocycles due to Avila and the author.
