Deviation of ergodic averages for rational polygonal billiards

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.

to appear in Duke Mathematical Journal. Some minor corrections made, typos fixed, some new references added

References in corpus (3)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Euler characteristics of Teichmüller curves in genus two
• Decay of Correlations for the Rauzy-Veech-Zorich Induction Map on the Space of Interval Exchange Transformations and the Central Limit Theorem for the Teichmueller Flow on the Moduli Space of Abelian Differentials