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Elliptical Billiards in the Minkowski Plane and Extremal Polynomials A. K. Adabraha, V. Dragovićba, M. Radnovićcb a Department of Mathematical Sciences, The University of Texas at Dallas, 800 West Campbell Road, 75080 Richardson TX, USA b Mathematical Institute SANU, Kneza Mihaila 36, 11001, Belgrade, p.p. 367, Serbia c School of Mathematics and Statistics, The University of Sydney, Carslaw F07, 2006 NSW, Australia Аннотация: We derive necessary and sufficient conditions for periodic trajectories of billiards within an ellipse in the Minkowski plane in terms of an underlying elliptic curve. Equivalent conditions are derived in terms of polynomial-functional equations as well. The corresponding polynomials are related to the classical extremal polynomials. Similarities and differences with respect to the previously studied Euclidean case are indicated. Ключевые слова: Minkowski plane, elliptical billiards, elliptic curve, Akhiezer polynomials
DOI: https://doi.org/10.20537/nd190401   Полный текст:
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Тип публикации: Статья MSC: 14H70, 41A10, 70H06, 37J35, 26C05 Поступила в редакцию: 05.06.2019 Принята в печать:26.08.2019 Язык публикации: английский Образец цитирования: A. K. Adabrah, V. Dragović, M. Radnović, “Elliptical Billiards in the Minkowski Plane and Extremal Polynomials”, Нелинейная динам., 15:4 (2019), 
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