Deviation of ergodic averages for rational polygonal billiards

2007/01/23 by Jayadev S. Athreya, Athreya, Jayadev S., Giovanni Forni +1
Mathematics · #37E35 #37F25 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.DS #math.GT #msc:37E35 #msc:37F25

paper · pdf · doi:10.48550/arxiv.math/0701658

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

openalex publication_date 2007/01/23 · arxiv created 2008/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Deviation for interval exchange transformations

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