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Deviation of ergodic averages for rational polygonal billiards

Jayadev S. Athreya·Giovanni Forni
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Abstract

We prove polynomial upper bounds for the deviation of ergodic averages for the straight line flow on every translation surface in almost every direction, in particular for those surfaces arising from rational polygonal billiards.

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Jayadev S. Athreya, Giovanni Forni. 2008-01-17. Deviation of ergodic averages for rational polygonal billiards. https://arxiv.org/abs/math/0701658

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