Busseman functions for the N-body problem

TL;DR

This paper demonstrates that Busemann functions associated with parabolic homothetic motions in the N-body problem serve as viscosity solutions to the Hamilton-Jacobi equation, with their calibrating curves asymptotically approaching these motions.

Contribution

It establishes a novel connection between Busemann functions and viscosity solutions in the context of the N-body problem, extending understanding of asymptotic behaviors.

Findings

Busemann functions are viscosity solutions of the Hamilton-Jacobi equation.

Calibrating curves tend to the homothetic motion asymptotically.

Provides a new analytical tool for studying the N-body problem.

Abstract

We prove that the Busemann function of the parabolic homotetic motion for a minimal central coniguration of the N-body problem is a viscosity solution of the Hamilton-Jacobi equation and that its calibrating curves are asymptotic to the homotetic motion.