The average length of a trajectory in a certain billiard in a flat two-torus

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We remove a small disc from the flat two-dimensional torus and consider a point-like particle that starts moving from the center of the disc with linear trajectory. We provide asymptotic estimates for the moments of the first exit time, with respect to the velocity, when the radius of the disc tends to zero.
28 pages, 5 figures

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Number Theory, Mathematical Physics, Dynamical Systems, 11B57; 82C40; 37D50; 58F25

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http://salesiana.dossiersoluciones.com/handle/123456789/62442

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0110208
 http://arxiv.org/abs/math/0110208
 New York J. Math. 9 (2003), 53-73

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arXiv