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Department of Mathematical Sciences, The University of Texas at Dallas
Adabrah A. K., Dragović V., Radnović M.
Elliptical Billiards in the Minkowski Plane and Extremal Polynomials
2019, Vol. 15, no. 4, pp. 397-407
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.