On Hoelder-continuity of Oseledets subspaces

TL;DR

This paper proves that Oseledets subbundles exhibit Hoelder continuity on large measure sets for certain cocycles, extending to vector bundle automorphisms and specific flows in moduli spaces.

Contribution

It establishes Hoelder continuity of Oseledets subbundles for non-invertible cocycles over Lipschitz transformations, extending previous results to broader contexts.

Findings

Oseledets subbundles are Hoelder-continuous on large measure sets.

Results apply to vector bundle automorphisms and Teichmueller flows.

Extends continuity results to non-invertible cocycles and moduli space dynamics.

Abstract

For Hoelder cocycles over a Lipschitz base transformation, possibly non-invertible, we show that the subbundles given by the Oseledets Theorem are Hoelder-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 Teichmueller flow on the moduli space of abelian differentials. Following a recent result of Chaika-Eskin, our results also extend to any given Teichmueller disk.