ELLIPSOIDAL BILLIARDS WITH ISOTROPIC HARMONIC POTENTIALS

DOI10.1142/S0218127400001316zbMath0984.37065WikidataQ62266583 ScholiaQ62266583MaRDI QIDQ4522204

Jan Wiersig

Publication date: 22 April 2002

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

integrable Hamiltonian systemellipsoidal billiardisotopic harmonic potential

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items (3)

The Jacobi-Rosochatius problem on an ellipsoid: the Lax representations and billiards ⋮ Resonance of ellipsoidal billiard trajectories and extremal rational functions ⋮ Periodic ellipsoidal billiard trajectories and extremal polynomials

Cites Work

• Discrete versions of some classical integrable systems and factorization of matrix polynomials
• Elliptic quantum billiard
• Triaxial ellipsoidal quantum billiards
• Elliptical billiards and Poncelet’s theorem
• Billiard systems on quadric surfaces and the Poncelet theorem
• Elliptical billiard systems and the full Poncelet’s theorem in n dimensions
• Elliptical billiards and hyperelliptic functions
• Billiard systems in three dimensions: the boundary integral equation and the trace formula
• ACTION INTEGRALS AND ENERGY SURFACES OF THE KOVALEVSKAYA TOP
• On integrable potential perturbations of the billiard system within an ellipsoid
• Linear stability in billiards with potential

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