Elliptical billiards in the Minkowski plane and extremal polynomials

Abstract

We derive necessary and sufficient conditions for periodic and for elliptic periodic trajectories of billiards within an ellipse in the Minkowski plane in terms of an underlining elliptic curve. Equivalent conditions are derived in terms of polynomial-functional equations as well. The corresponding polynomials are related to the classical extremal polynomials. The similarities and differences with respect to previously studied Euclidean case are indicated.