Billiards in rectangles with barriers

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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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Dynamical Systems, Mathematical Physics, 37A99 (primary) 37E15, 37D40, 37D50 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/61922

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0107204
 http://arxiv.org/abs/math/0107204

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arXiv