|Authors:||Adabrah, Anani Komla
|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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