Topological analysis of a billiard bounded by confocal quadrics in a potential field

DOI10.1070/SM9418zbMath1468.37028OpenAlexW3103997779MaRDI QIDQ4988798

S. E. Pustovoitov

Publication date: 19 May 2021

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm9418

zbMATH Keywords

integrable systemFomenko-Zieschang invariantHooke potentialLiouville equivalence

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (5)

Topological classification of billiards bounded by confocal quadrics in three-dimensional Euclidean space ⋮ Projective integrable mechanical billiards ⋮ Conformal transformations and integrable mechanical billiards ⋮ Topology of isoenergy 5-surfaces of a three-axial ellipsoid with a Hooke potential ⋮ Billiards with changing geometry and their connection with the implementation of the Zhukovsky and Kovalevskaya cases

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• New approach to symmetries and singularities in integrable Hamiltonian systems
• A topological invariant which roughly classifies integrable strictly nondegenerate Hamiltonians on four-dimensional symplectic manifolds
• Topological invariants of Liouville integrable Hamiltonian systems
• Some integrable extensions of Jacobi's problem of geodesics on an ellipsoid
• A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics
• Maximally symmetric cell decompositions of surfaces and their coverings
• A BORDISM THEORY FOR INTEGRABLE NONDEGENERATE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM. A NEW TOPOLOGICAL INVARIANT OF HIGHER-DIMENSIONAL INTEGRABLE SYSTEMS
• Integrable topological billiards and equivalent dynamical systems
• An elliptic billiard in a potential force field: classification of motions, topological analysis
• Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards

This page was built for publication: Topological analysis of a billiard bounded by confocal quadrics in a potential field