Generic linear cocycles over a minimal base

Volume 218 / 2013

Jairo Bochi Studia Mathematica 218 (2013), 167-188 MSC: Primary 37H15. DOI: 10.4064/sm218-2-4


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.


  • Jairo BochiDepartamento de Matemática
    Pontifícia Universidade Católica do Rio de Janeiro (PUC–Rio)
    Rio de Janeiro 22451-900, Brazil

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