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

@article{Trevio2010OnTN,
title={On the non-uniform hyperbolicity of the Kontsevich–Zorich cocycle for quadratic differentials},
author={Rodrigo Trevi{\~n}o},
journal={Geometriae Dedicata},
year={2010},
volume={163},
pages={311-338}
}
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…
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