Structural stability of homothetic solutions of the collinear n-body problem

Details Structural stability of homothetic solutions of the collinear n-body problem Structural stability of homothetic solutions of the collinear n-body problem

May 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..19..391d&link_type=abstract

Celestial Mechanics, vol. 19, May 1979, p. 391-404.

Mathematics

5

Many Body Problem, Orbital Mechanics, Particle Collisions, Systems Stability, Collinearity, Hamiltonian Functions, Manifolds (Mathematics)

Scientific paper

We investigate specific homothetic solutions of the n-body problem which both begin and end in a simultaneous collision of all of the particles. Under a suitable change of variables, these solutions become heteroclinic orbits, i.e., they lie in the intersection of the stable and unstable manifolds of distinct equilibrium points. Our main result is that these manifolds intersect transversely along these orbits. This proves that the homothetic solutions are structurally stable.

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