Billiards in ellipses revisited

DOI10.1007/s40879-020-00426-9OpenAlexW3086511936MaRDI QIDQ2095611

Arseniy V. Akopyan, Sergei Tabachnikov, Richard Evan Schwartz

Publication date: 17 November 2022

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.02934

zbMATH Keywords

complete integrabilityPoncelet polygonPoncelet gridelliptic billiardsMinkowski billiards

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geometric constructions in real or complex geometry (51M15) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (12)

Fifty new invariants of \(N\)-periodics in the elliptic billiard ⋮ Poncelet triangles: a theory for locus ellipticity ⋮ Estimating elliptic billiard invariants with spatial integrals ⋮ Invariant center power and elliptic loci of Poncelet triangles ⋮ Unnamed Item ⋮ The geometry of billiards in ellipses and their Poncelet grids ⋮ New invariants of Poncelet-Jacobi bicentric polygons ⋮ Isometric Billiards in Ellipses and Focal Billiards in Ellipsoids ⋮ Dan Reznik's identities and more ⋮ On the motion of billiards in ellipses ⋮ New Properties of Triangular Orbits in Elliptic Billiards ⋮ Poncelet plectra: harmonious curves in cosine space

Cites Work

• Unnamed Item
• The pentagram integrals for Poncelet families
• From symplectic measurements to the Mahler conjecture
• Integrable discrete-time systems and difference operators
• Billiards in Finsler and Minkowski geometries
• Can the elliptic billiard still surprise us?
• Elementary approach to closed billiard trajectories in asymmetric normed spaces
• Bounds for Minkowski Billiard Trajectories in Convex Bodies
• Poncelet Porisms and Beyond
• Integrable maps
• The Poncelet grid
• The Poncelet Grid and Billiards in Ellipses

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