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

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

2001-10-19

arxiv.org/abs/math/0110208v3

New York J. Math. 9 (2003), 53-73

Mathematics

Number Theory

28 pages, 5 figures

Scientific paper

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.

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