An ellipsoidal billiard with a quadratic potential

DOI10.1023/A:1012326828456zbMath1001.37044OpenAlexW2152094255MaRDI QIDQ5959534

Yuri N. Fedorov

Publication date: 15 April 2002

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1012326828456

zbMATH Keywords

billiard mapgeneralized JacobiansHooke potentiallimit values of meromorphic functions

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relationships between algebraic curves and integrable systems (14H70) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (12)

Virtual billiards in pseudo-Euclidean spaces: discrete Hamiltonian and contact integrability ⋮ The Jacobi-Rosochatius problem on an ellipsoid: the Lax representations and billiards ⋮ Resonance of ellipsoidal billiard trajectories and extremal rational functions ⋮ On elliptical billiards in the Lobachevsky space and associated geodesic hierarchies. ⋮ Projective integrable mechanical billiards ⋮ Non-uniform ergodic properties of Hamiltonian flows with impacts ⋮ Conformal transformations and integrable mechanical billiards ⋮ Heisenberg model in pseudo-Euclidean spaces. II. ⋮ Caustics of Poncelet polygons and classical extremal polynomials ⋮ Periodic ellipsoidal billiard trajectories and extremal polynomials ⋮ Periodic billiard orbits on \(n\)-dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations ⋮ On the structure of Hamiltonian impact systems

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