Authors: Adabrah, Anani Komla
Dragović, Vladimir 
Radnović, Milena
Title: Elliptical Billiards in the Minkowski plane and extremal polynomials
Journal: Russian Journal of Nonlinear Dynamics
Volume: 15
Issue: 4
First page: 397
Last page: 407
Issue Date: 1-Jan-2019
ISSN: 2658-5324
DOI: 10.20537/nd190401
Abstract: 
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.
Keywords: Akhiezer polynomials | Elliptic curve | Elliptical billiards | Minkowski plane
Publisher: Institute of Computer Science Izhevsk
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 

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