Generic uniqueness of the minimal Moulton central configuration

Abstract

We prove that, for generic (open and dense) values of the masses, the Newtonian potential function of the collinear N-body problem has $N!/2$ critical values when restricted to a fixed inertia level. In particular, we prove that for generic masses, there is only one minimal Moulton configuration.

References in corpus (2)

• Globally minimizing parabolic motions in the Newtonian N-body problem
• Busseman functions for the N-body problem

Cited by in corpus (3)

• The reduction on the linear stability of elliptic Euler-Moulton solutions of the n-body problem to those of 3-body problems
• Central Configurations and Mutual Differences
• Linear Stability of Elliptic Relative Equilibria of Restricted Four-body Problem