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Article

On Hölder-continuity of Oseledets subspaces

Journal of London Mathematical Society. 2016. Vol. 96. No. 1. P. 194-218.
Araujo V., Bufetov A. I., Filip S.

For Hölder cocycles over a Lipschitz base transformation, possibly non-invertible, we show that the subbundles given by the Oseledets Theorem are Hölder-continuous on compact sets of measure arbitrarily close to 1. The results extend to vector bundle automorphisms, as well as to the Kontsevich-Zorich cocycle over the Teichmüller flow on the moduli space of abelian differentials. Following a recent result of Chaika-Eskin, our results also extend to any given Teichmüller disk. © 2015 London Mathematical Society.