Elliptical billiards and hyperelliptic functions

DOI10.1063/1.530116zbMath0780.70015OpenAlexW2080547499MaRDI QIDQ4203213

Shau-Jin Chang, B. Crespi, Kang-jie Shi

Publication date: 8 September 1993

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

Full work available at URL: https://doi.org/10.1063/1.530116

zbMATH Keywords

periodic orbitsHamilton-Jacobi equationsphase spacetopologyRiemann surfaceverticesAbelian integralsPoncelet's theorem

Mathematics Subject Classification ID

Topological dynamics (37B99) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Elliptic functions and integrals (33E05) Collision of rigid or pseudo-rigid bodies (70F35)

Related Items (9)

ELLIPSOIDAL BILLIARDS WITH ISOTROPIC HARMONIC POTENTIALS ⋮ Complex Formulation of Poncelet Property in Numerical Range ⋮ Trajectory tracking for a particle in elliptical billiards ⋮ Universal hitting time statistics for integrable flows ⋮ Classification of symmetric periodic trajectories in ellipsoidal billiards ⋮ On periodical trajectories of the billiard systems within an ellipsoid in Rd and generalized Cayley’s condition ⋮ Triaxial ellipsoidal quantum billiards ⋮ Conditions of Cayley’s type for ellipsoidal billiard ⋮ Generalized Weierstrass kernels on the intersection of two complex hypersurfaces

Cites Work

• Elliptical billiards and Poncelet’s theorem
• Elliptical billiard systems and the full Poncelet’s theorem in n dimensions

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