N-body Scattering

Details N-body Scattering N-body Scattering

Jul 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dda....38.1405m&link_type=abstract

American Astronomical Society, DDA meeting #38, #14.05

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Scientific paper

For the positive energy N-body problem perhaps the simplest solutions are the strictly hyperbolic ones: the bodies come in from infinity at postive speeds, interact briefly, then recede outwards again, each body asymptotic to a different ray. The asymptotics of these solutions were worked out by Chazy. Given a set of N distinct rays for the distant past, and another set of such rays for the distant future, does there exist a solution connecting the set of past rays to the set of future rays? We will sketch how the gluing method of nonlinear elliptic PDE theory yields an affirmative answer. We also discuss the failure of a naive variational method for resolving this question, and ammendments to the variational method which might yield an affirmative answer to refinements of the question.

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