Existence of partially hyperbolic motions in the N-body problem

TL;DR

This paper proves the existence of certain special motions in the Newtonian N-body problem that are partially hyperbolic, collisionless, and minimize action, providing new insights into the dynamics of such systems.

Contribution

It establishes the existence of partially hyperbolic motions with prescribed energy and initial conditions, which are also free time minimizers and geodesic rays in the Jacobi-Maupertuis metric.

Findings

Existence of partially hyperbolic motions in N-body problem.

These motions are collisionless and have prescribed positive energy.

They are characterized as free time minimizers and geodesic rays.

Abstract

In the context of the Newtonian N-body problem, we prove the existence of a partially hyperbolic motion with prescribed positive energy and any initial collisionless configuration. Moreover, it is a free time minimizer of the respective supercritical Newtonian action or equivalently a geodesic ray for the respective Jacobi-Maupertuis metric.