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Billiards in rectangles with barriers

Alex Eskin·Howard Masur·Martin Schmoll
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Abstract

We use Ratner's theorem to compute the asymptotics of the number of (cylinders of) periodic trajectories in a rectangle with a barrier, assuming that the location p/q of the barrier is rational. We also show that as q tends to infinity, the constant in the asymptotic formula tends to the constant for the generic genus 2 flat surface.

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Alex Eskin, Howard Masur, Martin Schmoll. 2001-07-28. Billiards in rectangles with barriers. https://arxiv.org/abs/math/0107204

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