Compactification of the energy surfaces for n bodies

TL;DR

This paper introduces a method to compactify energy surfaces in n-body problems, resulting in a manifold with corners where the flow is globally defined, aiding the analysis of the system's dynamics.

Contribution

It develops a new compactification technique for energy surfaces in n-body systems, extending the understanding of their geometric and dynamical properties.

Findings

Constructed a compactification of energy surfaces as manifolds with corners.

Established that the flow becomes globally defined after a time change.

Provided a framework for analyzing n-body dynamics on these compactified manifolds.

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.