Billiards in rectangles with barriers

Details Billiards in rectangles with barriers Billiards in rectangles with barriers

2001-07-28

arxiv.org/abs/math/0107204v1

Mathematics

Dynamical Systems

Scientific paper

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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