Geometriae Dedicata

, Volume 163, Issue 1, pp 311–338 | Cite as

On the non-uniform hyperbolicity of the Kontsevich–Zorich cocycle for quadratic differentials

Original Paper

Abstract

We prove the non-uniform hyperbolicity of the Kontsevich–Zorich cocycle for a measure supported on abelian differentials which come from non-orientable quadratic differentials through a standard orienting, double cover construction. The proof uses Forni’s criterion (J. Mod. Dyn. 5(2):355–395, 2011) for non-uniform hyperbolicity of the cocycle for \({SL(2, \mathbb{R})}\)-invariant measures. We apply these results to the study of deviations in homology of typical leaves of the vertical and horizontal (non-orientable) foliations and deviations of ergodic averages.

Keywords

Quadratic differentials Kontsevich–Zorich cocycle Non-orientable foliations 

Mathematics Subject Classification

32G15 37D25 

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsThe University of MarylandCollege ParkUSA

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