97-152 D.Burago, F.Ferleger, A.Kononenko
Uniform estimates on the number of collisions in semi-dispersing billiards. (38K, Latex 2e) Apr 1, 97
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Abstract. We use the methods of non-standard Riemannian geometry to obtain complete solutions of two classic billiard problems: 1. We establish local uniform estimates on the number of collisions in non-degenerate semi-dispersing billiards (moreover, our results apply to billiards on arbitrary manifolds). 2. We find an explicit uniform estimate on the maximal possible number of collisions, in the infinite period of time, in an arbitrary system of hard spheres in empty space, in terms of the number of spheres, their masses and radii. Our methods are based on the construction of a certain Alexandrov space of curvature bounded from above which geodesics naturally correspond to the trajectories of the billiard flow.

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