Elliptical billiards and Poncelet’s theorem
From MaRDI portal
Publication:3814877
DOI10.1063/1.527900zbMath0663.70015OpenAlexW1990585029MaRDI QIDQ3814877
Richard M. Friedberg, Shau-Jin Chang
Publication date: 1988
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.527900
Poncelet theoremconfocal conicscaustic quadricsellipsoidal boundariesthree-dimensional billiard systems
Related Items
ELLIPSOIDAL BILLIARDS WITH ISOTROPIC HARMONIC POTENTIALS ⋮ Limit sets of convex non-elastic billiards ⋮ The billiard inside an ellipse deformed by the curvature flow ⋮ On the local Birkhoff conjecture for convex billiards ⋮ Complex Formulation of Poncelet Property in Numerical Range ⋮ Chaotic properties of the elliptical stadium ⋮ Robin spectral rigidity of the ellipse ⋮ Liouville integrable generalized billiard flows and Poncelet type theorems ⋮ Veiled assonance between geodesics on ellipsoid and billiard in its focal ellipse ⋮ The Elliptic Integral Machine: A Collision-based Model of Computation ⋮ A survey of the analytical description of periodic elliptical billiard trajectories ⋮ On integrable potential perturbations of the billiard system within an ellipsoid ⋮ On the integrability of Birkhoff billiards ⋮ Closed geodesics and billiards on quadrics related to elliptic KdV solutions ⋮ Billiard systems on quadric surfaces and the Poncelet theorem ⋮ Nearly circular domains which are integrable close to the boundary are ellipses ⋮ Exponentially Small Asymptotic Formulas for the Length Spectrum in Some Billiard Tables ⋮ Classification of symmetric periodic trajectories in ellipsoidal billiards ⋮ Rational Poncelet ⋮ On periodical trajectories of the billiard systems within an ellipsoid in Rd and generalized Cayley’s condition ⋮ Triaxial ellipsoidal quantum billiards ⋮ Elliptical billiard systems and the full Poncelet’s theorem in n dimensions ⋮ Elliptical billiards and hyperelliptic functions ⋮ On the integrability of strictly convex billiard tables with boundaries close to ellipses with small eccentricities ⋮ Elliptic quantum billiard ⋮ Perturbations of elliptic billiards ⋮ Conditions of Cayley’s type for ellipsoidal billiard ⋮ On some invariants of Birkhoff billiards under conjugacy ⋮ Static and time-dependent perturbations of the classical elliptical billiard. ⋮ Non-persistence of resonant caustics in perturbed elliptic billiards ⋮ Inverse problems and rigidity questions in billiard dynamics
Cites Work