Globally minimizing parabolic motions in the Newtonian N-body problem

Abstract

We consider the $N$-body problem in ${\mathbb{R}}^d$ with the newtonian potential $1/r$. We prove that for every initial configuration $x_i$ and for every minimizing normalized central configuration $x_0$, there exists a collision-free parabolic solution starting from $x_i$ and asymptotic to $x_0$. This solution is a minimizer in every time interval. The proof exploits the variational structure of the problem, and it consists in finding a convergent subsequence in a family of minimizing trajectories. The hardest part is to show that this solution is parabolic and asymptotic to $x_0$.

26 pages, 2 figures

References in corpus (1)

• On weak KAM theory for N-body problems

Cited by in corpus (1)

• On weak KAM theory for N-body problems