A generalization of Bertrand's theorem to surfaces of revolution

DOI10.1070/SM2012v203n08ABEH004257zbMath1408.53115arXiv1109.0745MaRDI QIDQ4650146

D. A. Fedoseev, O. A. Zagryadskii, E. A. Kudryavtseva

Publication date: 23 November 2012

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

Full work available at URL: https://arxiv.org/abs/1109.0745

zbMATH Keywords

surface of revolutionclosed orbitsBertrand's theoreminverse problem of dynamicsmotion in a central field

Mathematics Subject Classification ID

Symplectic geometry, contact geometry (53Dxx)

Related Items (15)

The Bertrand's manifolds with equators ⋮ Darboux inversions of the Kepler problem ⋮ Keplerian Dynamics on the Heisenberg Group and Elsewhere ⋮ Superintegrable Bertrand natural mechanical systems ⋮ Noncompact bifurcations of integrable dynamic systems ⋮ Scattering invariants in Euler’s two-center problem ⋮ Geometry, dynamics and different types of orbits ⋮ Bifurcation diagrams of natural Hamiltonian systems on Bertrand manifolds ⋮ Bertrand surfaces with a pseudo-Riemannian metric of revolution ⋮ The spatial problem of 2 bodies on a sphere. Reduction and stochasticity ⋮ Superintegrable Bertrand magnetic geodesic flows ⋮ A proof of Bertrand's theorem using the theory of isochronous potentials ⋮ The global and local realizability of Bertrand Riemannian manifolds as surfaces of revolution ⋮ The relations between the Bertrand, Bonnet, and Tannery classes ⋮ The explicit form of the Bertrand metric

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