Caustics of Poncelet polygons and classical extremal polynomials

DOI10.1134/S1560354719010015zbMath1432.37055arXiv1812.02907OpenAlexW2963085925WikidataQ128492459 ScholiaQ128492459MaRDI QIDQ1739578

Milena Radnović, Vladimir Dragović

Publication date: 26 April 2019

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

Full work available at URL: https://arxiv.org/abs/1812.02907

zbMATH Keywords

Chebyshev polynomialselliptic curvesextremal polynomialsperiodic trajectoriescausticsPoncelet polygonsZolotarev polynomialsPell's equationsAkhiezer polynomialsCayley conditionsdiscriminantly separable polynomialselliptical billiards

Mathematics Subject Classification ID

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) Real polynomials: analytic properties, etc. (26C05) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (11)

Complex caustics of the elliptic billiard ⋮ Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials ⋮ 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 ⋮ Periodic ellipsoidal billiard trajectories and extremal polynomials ⋮ The Ballet of Triangle Centers on the Elliptic Billiard ⋮ Deformations of the Zolotarev polynomials and Painlevé VI equations ⋮ Periodic billiards within conics in the Minkowski plane and Akhiezer polynomials ⋮ New Properties of Triangular Orbits in Elliptic Billiards

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