Abstract
We prove a polynomial upper bound on the deviation of ergodic averages for almost all directional flows on every translation surface, in particular, for the generic directional flow of billiards in any Euclidean polygon with rational angles
Citation
J. S. Athreya. G. Forni. "Deviation of ergodic averages for rational polygonal billiards." Duke Math. J. 144 (2) 285 - 319, 15 August 2008. https://doi.org/10.1215/00127094-2008-037
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