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 \(\big{(}2d(n-1)-1\big{)}\)-dimensional manifold with corners in the sense of Melrose. After a time change, the flow on this manifold is globally defined and nontrivial on the boundary.