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Periodic billiard orbits in right triangle

Serge Troubetzkoy
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Abstract

There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.

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Serge Troubetzkoy. 2004-05-14. Periodic billiard orbits in right triangle. https://arxiv.org/abs/math/0405280

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