Compactification of the energy surfaces for n bodies

Abstract

For n bodies moving in Euclidean d-space under the influence of a homogeneous pair interaction we compactify every center-of-mass energy surface, obtaining a 2d(n -1)-1 - dimensional manifold with corners in the sense of Melrose. After a time change, the flow on this manifold is globally defined and non-trivial on the boundary.

44 pages, 10 figures, submitted to Alain Chenciner's 80th birthday conference proceedings to be published in Regular and Chaotic Dynamics