Morse index properties of colliding solutions to the \(N\)-body problem

DOI10.1016/J.ANIHPC.2007.02.005zbMath1143.70006arXivmath/0609837OpenAlexW2006724333MaRDI QIDQ930018

Vivina Barutello, Simone Secchi

Publication date: 19 June 2008

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609837

zbMATH Keywords

singular Hamiltonian systemnon-minimalityvariational index

Mathematics Subject Classification ID

(n)-body problems (70F10) Collisions in celestial mechanics, regularization (70F16)

Related Items (13)

Free time minimizers for the three-body problem ⋮ An index theory for zero energy solutions of the planar anisotropic Kepler problem ⋮ An index theory for collision, parabolic and hyperbolic solutions of the Newtonian \(n\)-body problem ⋮ Symbolic dynamics for the anisotropic \(N\)-centre problem at negative energies ⋮ An index theory for asymptotic motions under singular potentials ⋮ Entire minimal parabolic trajectories: the planar anisotropic Kepler problem ⋮ Minimizing configurations and Hamilton-Jacobi equations of homogeneous \(N\)-body problems ⋮ Linear instability of relative equilibria for \(n\)-body problems in the plane ⋮ Application of Morse index in weak forceN-body problem ⋮ On the minimizing triple collision orbits in the planar Newtonian three-body problem ⋮ Collision index and stability of elliptic relative equilibria in planar \(n\)-body problem ⋮ Minimal geodesics of the isosceles three body problem ⋮ Geodesic rays of the \(N\)-body problem

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