Multifold Kepler systems—Dynamical systems all of whose bounded trajectories are closed

DOI10.1063/1.531086zbMath0832.70010OpenAlexW2033076481MaRDI QIDQ4836943

Noriaki Katayama, Toshihiro Iwai

Publication date: 7 March 1996

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

Full work available at URL: https://doi.org/10.1063/1.531086

zbMATH Keywords

configuration spaceRunge-Lenz vectorBertrand methodDirac's monopolespherically symmetric Hamiltonian system

Mathematics Subject Classification ID

Two-body problems (70F05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

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The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories, A new exactly solvable quantum model in \(N\) dimensions, On two superintegrable nonlinear oscillators in \(N\) dimensions, Dynamical and symmetry groups of the \(SU (2)\) Kepler problem, An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric, Superintegrable systems on spaces of constant curvature, MICZ-Kepler systems in noncommutative space and duality of force laws, Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability, Superintegrability on \(N\)-dimensional curved spaces: central potentials, centrifugal terms and monopoles, Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds, Laplace–Runge–Lenz symmetry in general rotationally symmetric systems, A new discretization of the Kepler motion which conserves the Runge-Lenz vector, HIDDEN SYMMETRIES IN A GAUGE-COVARIANT APPROACH, HAMILTONIAN REDUCTION AND OXIDATION

Cites Work

• A remark on the scattering of BPS monopoles.
• Low energy scattering of nonabelian monopoles.
• On extended Taub-NUT metrics
• The hidden symmetries of multi-centre metrics
• Kepler-type dynamical symmetries of long-range monopole interactions
• The four-dimensional conformal Kepler problem reduces to the three-dimensional Kepler problem with a centrifugal potential and Dirac’s monopole field. Classical theory
• The O(3,1) symmetry problem of the charge–monopole interaction
• The quantised MIC-Kepler problem and its symmetry group for negative energies
• Search for periodic Hamiltonian flows: A generalized Bertrand’s theorem
• Two classes of dynamical systems all of whose bounded trajectories are closed
• A dynamical group Su(2,2) and its use in the MIC-Kepler problem
• Two kinds of generalized Taub-NUT metrics and the symmetry of associated dynamical systems
• Search for a Universal Symmetry Group in Two Dimensions