Geodesic rays of the $N$-body problem

Abstract

For the Newtonian N-body problem, we study the Jacobi-Maupertuis metric of the nonnegative energy levels. We show that the geodesic rays are expansive, that is to say, all the distances between the bodies must be divergent functions. More precisely, we prove that the evolution of such motions asymptotically decomposes into free particles and subsystems in completely parabolic expansion. The theorem applies in particular to the maximal characteristic curves of any given global viscosity solution of the stationary Hamilton-Jacobi equation $H(x,d_{x}u)=h$.

arXiv comment20 pages

References in corpus (7)

• On the Existence of Collisionless Equivariant Minimizers for the Classical n-body Problem
• On weak KAM theory for N-body problems
• On the free time minimizers of the Newtonian N-body problem
• Chazy-Type Asymptotics and Hyperbolic Scattering for the $n$-Body Problem
• Busseman functions for the N-body problem
• Free time minimizers for the planar three-body problem
• Minimizing configurations and Hamilton-Jacobi equations of homogeneous N-body problems