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arXiv · 1507.06635

Polygonal billiards and "optical tori"

Eduardo Díaz-Miguel
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Abstract

We give an optical physicist view of the problem of the trajectories in a polygonal billiard using only basic facts of Optics and the theory of functions of a complex variable. This approach allow us to stablish a certain correspondence between n-gon billiards and one-holed 2n-punctured tori. Therefore the existence of periodic trajectories in a certain polygon becomes the problem of the existence of closed geodesics in its associated torus.

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Eduardo Díaz-Miguel. 2015-07-16. Polygonal billiards and "optical tori". https://arxiv.org/abs/1507.06635

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