Pablo S. Casas: Clasification of symmetric periodic trajectories of billiards inside ellipsoids

We find and classify nonsingular symmetric periodic trajectories
(SPTs) of billiards inside nondegenerate ellipsoids of R^{n+1} for
n=1,2. SPTs are periodic trajectories passing through some symmetry
set. We prove that there are exactly 2^{2n}(2^{n+1}-1) classes of such
trajectories. We have implemented an algorithm to find minimal SPTs of
each of the 12 classes in the 2D case (n=1) and each of the 112
classes in the 3D case (n=2). They have periods 3, 4 or 6 in the 2D
case; and 4, 5, 6, 8 or 10 in the 3D case. We display the 12 classes
in the 2D case and a selection of 3D minimal SPTs.

This is a joint work with Rafael Ramírez Ros.

http://www.ma.utexas.edu/mp_arc/c/11/11-192.pdf