Regul. Chaotic Dyn., 2023 Volume 28, Issue 1, Pages 14–43
(Mi rcd1193)
This article is cited in
2 papers
Billiards Within Ellipsoids in the 4-Dimensional
Pseudo-Euclidean Spaces Vladimir Dragović ab ,
Milena Radnović ca a Mathematical Institute SANU,
Kneza Mihaila 36, 11000 Beograd, p. p. 367, Serbia b The University of Texas in Dallas,
Department of Mathematical Sciences,
800 W. Campbell Rd, 75080-3021 Richardson TX, USA c The University of Sydney,
School of Mathematics and Statistics,
Carslaw F07, 2006 NSW, Australia Abstract:
We study billiard systems within an ellipsoid in the 4-dimensional pseudo-Euclidean
spaces. We provide an analysis and description of periodic and weak periodic trajectories in
algebro-geometric and functional-polynomial terms.
Keywords:
ellipsoidal billiards, caustics, confocal families of quadrics, extremal polynomials,
periodic trajectories, Poncelet porism.
MSC: 37J35 ,
37D50 ,
14H70 ,
26C05 ,
41A10 ,
70H06 Received: 29.11.2022
Accepted: 05.01.2023
Language: English
DOI:
10.1134/S1560354723010033
© , 2026
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