The Ballet of Triangle Centers on the Elliptic Billiard

zbMath1453.37024arXiv2002.00001MaRDI QIDQ5118043

Jair Koiller, Dan Reznik, Ronaldo A. Garcia

Publication date: 4 September 2020

Full work available at URL: https://arxiv.org/abs/2002.00001

zbMATH Keywords

periodic trajectoriesdynamic geometrytriangle centerelliptic billiardloci

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (5)

More about areas and centers of Poncelet polygons ⋮ Fifty new invariants of \(N\)-periodics in the elliptic billiard ⋮ Loci of 3-periodics in an Elliptic Billiard: why so many ellipses? ⋮ Poncelet triangles: a theory for locus ellipticity ⋮ The talented Mr. inversive triangle in the elliptic billiard

Cites Work

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• Caustics of Poncelet polygons and classical extremal polynomials
• Can the elliptic billiard still surprise us?
• Polynomial triangle centers on the line at infinity
• On the incenters of triangular orbits on elliptic billiards
• The billiard ball problem on a table with a convex boundary - An illustrative dynamical problem. I. The invariant integral
• The Universe of Conics
• THE EXISTENCE OF CAUSTICS FOR A BILLIARD PROBLEM IN A CONVEX DOMAIN
• On the integrability of Birkhoff billiards
• An Introduction to Mathematical Billiards
• Projective Configuration Theorems: Old Wine into New Wineskins
• Elliptic Billiards and Ellipses Associated to the 3-Periodic Orbits
• The Poncelet Grid and Billiards in Ellipses

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