| Abstract: |
| Hyperbolic orbits of the Newtonian n-body problem are that for which the distances between the bodies tend to infinity with non-zero speed. Through a McGehee type blow-up, a manifold can be constructed at infinity containing normally hyperbolic manifolds of equilibria. The hyperbolic orbits are contained in the stable/unstable manifolds of these equilibria. Consequently, by analyzing the flow at and near infinity, we are able to construct a new proof of the analytic asymptotic expansions of Chazy for these solutions. Moreover, through this approach, we are able to set up a scattering map associated to solutions hyperbolic in both time directions.
This is joint work with Guowei Yu, Richard Montgomery and Rick Moeckel. |
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