Conditions of Cayley’s type for ellipsoidal billiard

DOI10.1063/1.532317zbMath0999.37019OpenAlexW2030657673MaRDI QIDQ4212654

Vladimir Dragović, Milena Radnović

Publication date: 6 November 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532317

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Projective techniques in algebraic geometry (14N05)

Related Items (11)

Bicentennial of the Great Poncelet Theorem (1813–2013): Current advances ⋮ Resonance of ellipsoidal billiard trajectories and extremal rational functions ⋮ On elliptical billiards in the Lobachevsky space and associated geodesic hierarchies. ⋮ A survey of the analytical description of periodic elliptical billiard trajectories ⋮ Pseudo-Euclidean billiards within confocal curves on the hyperboloid of one sheet ⋮ Trajectory tracking for a particle in elliptical billiards ⋮ Hyperelliptic Jacobians as billiard algebra of pencils of quadrics: Beyond Poncelet porisms ⋮ Periodic ellipsoidal billiard trajectories and extremal polynomials ⋮ Classification of symmetric periodic trajectories in ellipsoidal billiards ⋮ Geometry of integrable billiards and pencils of quadrics ⋮ On periodical trajectories of the billiard systems within an ellipsoid in Rd and generalized Cayley’s condition

Cites Work

• Integrable Lagrangian correspondences and the factorization of matrix polynomials
• Integrable discrete-time systems and difference operators
• Elliptical billiards and Poncelet’s theorem
• Elliptical billiard systems and the full Poncelet’s theorem in n dimensions
• Elliptical billiards and hyperelliptic functions
• On integrable potential perturbations of the billiard system within an ellipsoid

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