Authors: Dragović, Vladimir 
Radnović, Milena
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Cayley-type: Conditions for billiards within k quadrics in ℝ d
Journal: Journal of Physics A: Mathematical and General
Volume: 37
Issue: 4
First page: 1269
Last page: 1276
Issue Date: 30-Jan-2004
Rank: M21
ISSN: 0305-4470
DOI: 10.1088/0305-4470/37/4/014
Abstract: 
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 ℝ d is obtained.
Publisher: IOP Science

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