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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 1, Pages 14–43
DOI: https://doi.org/10.1134/S1560354723010033 (Mi rcd1193) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Billiards Within Ellipsoids in the 4-Dimensional Pseudo-Euclidean Spaces

Vladimir Dragovićab, Milena Radnovićca

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
Citations (1)
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DOI: https://doi.org/10.1134/S1560354723010033
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.
Funding agency Grant number
Australian Research Council DP190101838
Simons Foundation 854861
Science Fund of the Republic of Serbia 7744592
The research was supported by the Australian Research Council, Discovery Project #DP190101838 Billiards within quadrics and beyond, by the Simons Foundation grant no. 854861, by the Mathematical Institute of the Serbian Academy of Sciences and Arts, the Science Fund of Serbia grant Integrability and Extremal Problems in Mechanics, Geometry and Combinatorics, MEGIC, Grant No. 7744592 and the Ministry for Education, Science, and Technological Development of Serbia.
Received: 29.11.2022
Accepted: 05.01.2023
Bibliographic databases:
Document Type: Article
MSC: 37J35, 37D50, 14H70, 26C05, 41A10, 70H06
Language: English
Citation: Vladimir Dragović, Milena Radnović, “Billiards Within Ellipsoids in the 4-Dimensional Pseudo-Euclidean Spaces”, Regul. Chaotic Dyn., 28:1 (2023), 14–43
Citation in format AMSBIB
\Bibitem{DraRad23}
\by Vladimir Dragovi\'c, Milena Radnovi\'c
\paper Billiards Within Ellipsoids in the 4-Dimensional
Pseudo-Euclidean Spaces
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 1
\pages 14--43
\mathnet{http://mi.mathnet.ru/rcd1193}
\crossref{https://doi.org/10.1134/S1560354723010033}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4559067}
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  • https://www.mathnet.ru/eng/rcd/v28/i1/p14
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:34
     
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