Keplerian Dynamics on the Heisenberg Group and Elsewhere

DOI10.1007/978-1-4939-2441-7_14zbMath1342.70041arXiv1212.2713OpenAlexW2963457529MaRDI QIDQ3463522

Corey Shanbrom, Richard Montgomery

Publication date: 19 January 2016

Published in: Geometry, Mechanics, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.2713

zbMATH Keywords

Heisenberg grouptwo-body problemsub-Riemannian geometryHamiltonian mechanicsdilationsinteger latticeKepler's laws

Mathematics Subject Classification ID

Hamilton's equations (70H05) Two-body problems (70F05) Nilpotent and solvable Lie groups (22E25) Celestial mechanics (70F15) Sub-Riemannian geometry (53C17) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Related Items (7)

Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2 ⋮ On the \(n\)-body problem on surfaces of revolution ⋮ Non-integrability of the Kepler and the two-body problems on the Heisenberg group ⋮ Self-similarity in the Kepler-Heisenberg problem ⋮ Periodic orbits in the Kepler-Heisenberg problem ⋮ Numerical Methods and Closed Orbits in the Kepler–Heisenberg Problem ⋮ On then-body problem in R4

Cites Work

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• The \(n\)-body problem in spaces of constant curvature. II: Singularities
• Projective dynamics and classical gravitation
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• A generalization of Bertrand's theorem to surfaces of revolution
• The non-existence of centre-of-mass and linear-momentum integrals in the curved N-body problem
• Nonintegrability of the two-body problem in constant curvature spaces
• Gravitational and harmonic oscillator potentials on surfaces of revolution
• A fundamental solution for a subelliptic operator
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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