The average length of a trajectory in a certain billiard in a flat twotorus
Abstract
We remove a small disc from the flat twodimensional torus and consider a pointlike 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:math/0110208
 Bibcode:
 2001math.....10208B
 Keywords:

 Mathematics  Number Theory;
 Mathematical Physics;
 Mathematics  Dynamical Systems;
 Mathematics  Mathematical Physics;
 11B57;
 82C40;
 37D50;
 58F25
 EPrint:
 28 pages, 5 figures