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Session S03 - Geometric and Variational Methods in Celestial Mechanics

Monday, July 12, 12:00 ~ 12:25 UTC-3

Hyperbolic Solutions and Scattering in Newtonian n-Body Problem

Guowei Yu

Nankai University, China   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In the Newtonian n-body problem, the hyperbolic solutions are those all mutual distances between the masses tend to infinity with nonzero speed as time goes to negative or positive infinity. By using a variation of the McGehee coordinates, we show these solutions form the stable or unstable manifolds of some equilibria at infinity. This allows us to give a new proof of Chazy's classical asymptotic formulas for these solutions. In the second part of the talk we will consider bi-hyperbolic solutions, which means solutions that are hyperbolic in both forward and backward time. We will discuss the possible pairs of equilibria at infinity that are connected by a given bi-hyperbolic solution. This is a joint work with N. Duignan, R. Moeckel and R. Montgomery.

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