Integral manifolds of the \(N\)-body problem

DOI10.1007/BF01232677zbMath0801.70008MaRDI QIDQ1319201

Alain Albouy

Publication date: 24 November 1994

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144155

zbMATH Keywords

reductioncritical pointsangular momentumenergy functioncritical points at infinityplanar problemspatial problem

Mathematics Subject Classification ID

Applications of dynamical systems (37N99) (n)-body problems (70F10)

Related Items (16)

Finiteness of relative equilibria of the four-body problem ⋮ Critical points of the integral map of the charged three-body problem ⋮ Spatial equilateral chain central configurations of the five-body problem with a homogeneous potential ⋮ The global phase space for the 2- and 3-dimensional Kepler problems ⋮ The Lagrange reduction of the \(n\)-body problem, a survey ⋮ The integral manifolds of the \(N\) body problem ⋮ Symmetric central configurations and the inverse problem ⋮ New equations for central configurations and generic finiteness ⋮ Symmetry reduction of the 3-body problem in \(\mathbb{R}^4\) ⋮ On the uniqueness of trapezoidal four-body central configurations ⋮ Seven-body central configurations: a family of central configurations in the spatial seven-body problem ⋮ The optimal upper bound on the number of generalized Euler configurations ⋮ Planar \(N\)-body central configurations with a homogeneous potential ⋮ A century-long loop. ⋮ Equilateral chains and cyclic central configurations of the planar five-body problem ⋮ Critical points at infinity in charged \(N\)-body systems

Cites Work

• Central configurations of the N-body problem via equivariant Morse theory
• Some topology of n-body problems
• Topology and mechanics. I
• Topology and mechanics. II: The planar \(n\)-body problem
• On the integral manifolds of the n-body problem
• From rotations and inclinations to zero configurational velocity surfaces, II. The best possible configurational velocity surfaces
• Characteristic Classes. (AM-76)
• A generalized Morse theory
• Unnamed Item
• Unnamed Item

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