3 papers
math.DS2022
A Central Limit Theorem for the Kontsevich-Zorich Cocycle
Hamid Al-Saqban, Giovanni Forni
We show that a central limit theorem holds for exterior powers of the Kontsevich-Zorich (KZ) cocycle. In particular, we show that, under the hypothesis that the top Lyapunov expone…
math.DS2021
Oscillations and the Kontsevich-Zorich cocycle
Hamid Al-Saqban
We present a mechanism for producing oscillations along the lift of the Teichmüller geodesic flow to the (real) Hodge bundle, as the basepoint surface is deformed by a unipotent el…
math.DS2017
Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension
Hamid Al-Saqban, Paul Apisa, Alena Erchenko +3
We prove that for every flat surface , the Hausdorff dimension of the set of directions in which Teichmüller geodesics starting from exhibit a definite amount of deviation f…