Cayley-Type Conditions for Billiards within k Quadrics in Rᵈ

الأصل · EN

The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical trajectories for the billiard in the region bounded by k quadrics in Rᵈ and for the billiard ordered game within k ellipsoids in Rᵈ are derived. In a limit, the condition describing periodic trajectories of billiard systems on a quadric in Rᵈ is obtained.