On Estimates of the Number of Collisions for Billiards in Polyhedral Angles

Details On Estimates of the Number of Collisions for Billiards in Polyhedral Angles On Estimates of the Number of Collisions for Billiards in Polyhedral Angles

2006-10-08

arxiv.org/abs/math/0610257v1

Mathematics

Dynamical Systems

6 pages

Scientific paper

We obtain an upper bound of the number of collisions of any billiard
trajectory in a polyhedral angle in terms of the minimal eigenvalue of a
positive definite matrix which characterizes the angle. Elements of the matrix
are scalar products between the unit normal vectors of faces of the angle.

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