Periodic billiards within conics in the Minkowski plane and Akhiezer polynomials

DOI10.1134/S1560354719050034zbMath1436.37036arXiv1906.04911MaRDI QIDQ2305010

Milena Radnović, Anani Komla Adabrah, Vladimir Dragović

Publication date: 10 March 2020

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.04911

zbMATH Keywords

Chebyshev polynomialsextremal polynomialsperiodic trajectoriesMinkowski planeAkhiezer polynomialsdiscriminantly separable polynomialselliptic billiardsrelativistic conics

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relationships between algebraic curves and integrable systems (14H70) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Approximation by polynomials (41A10) Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions (37J38) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (6)

Complex caustics of the elliptic billiard ⋮ Resonance of ellipsoidal billiard trajectories and extremal rational functions ⋮ Combinatorics of periodic ellipsoidal billiards ⋮ Billiards within ellipsoids in the 4-dimensional pseudo-Euclidean spaces ⋮ Elliptical Billiards in the Minkowski Plane and Extremal Polynomials ⋮ Deformations of the Zolotarev polynomials and Painlevé VI equations

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