The manifold structure for collision and for hyperbolic-parabolic orbits in the n-body problem

DOI10.1016/0022-0396(84)90072-XzbMath0571.70009MaRDI QIDQ1061515

Donald G. Saari

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

asymptotic propertiesparabolic orbitscomplex analytic classification of a collision singularitytotal collapses

Mathematics Subject Classification ID

(n)-body problems (70F10) Collision of rigid or pseudo-rigid bodies (70F35)

Related Items (16)

Entire parabolic trajectories as minimal phase transitions ⋮ Periodic solutions with alternating singularities in the collinear four-body problem ⋮ Symbolic dynamics for the anisotropic \(N\)-centre problem at negative energies ⋮ An index theory for asymptotic motions under singular potentials ⋮ The existence of oscillatory and superhyperbolic motion in Newtonian systems ⋮ Investigating total collisions of the Newtonian N-body problem on shape space ⋮ Collective branch regularization of simultaneous binary collisions in the 3D N-body problem ⋮ Regularization of simultaneous binary collisions in the \(n\)-body problem ⋮ A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses ⋮ From rotations and inclinations to zero configurational velocity surfaces I. A natural rotating coordinate system ⋮ The flow of the \(N\)-body problem near a simultaneous-binary-collision singularity and integrals of motion on the collision manifold ⋮ Central configurations with many small masses ⋮ The Broucke–Hénon orbit and the Schubart orbit in the planar three-body problem with two equal masses ⋮ On the \(C^{8/3}\)-regularisation of simultaneous binary collisions in the collinear 4-body problem ⋮ On simultaneous binary collisions in the planar \(n\)-body problem ⋮ Star pentagon and many stable choreographic solutions of the Newtonian 4-body problem

Cites Work

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• Singularities and collisions of Newtonian gravitational systems
• On the role and the properties ofn body central configurations
• Collisions are of First Category
• On the real singularities of the N-body problem.
• Expanding Gravitational Systems
• Invariant manifolds

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