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arXiv · 1904.05186

Straightening Billiard Trajectories in Flat Disks and Katok-Zemlyakov Construction

İsmail Sağlam
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Abstract

We provide a method to straighten each billiard trajectory in a flat disk. As an application, we show that for each point on the disk and for almost all directions, the closure of the corresponding billiard trajectory contains a vertex. We generalize Katok-Zemlyakov construction to the flat disks with rational angle data: for each rational flat disk we obtain a translation surface and a projection to the doubling of the disk. We calculate the Euler characteristics of this translation surface.

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İsmail Sağlam. 2019-04-09. Straightening Billiard Trajectories in Flat Disks and Katok-Zemlyakov Construction. https://arxiv.org/abs/1904.05186

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