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 $x_0$.

arXiv comment26 pages, 2 figures

References in corpus (3)

• On the Existence of Collisionless Equivariant Minimizers for the Classical n-body Problem
• Action minimizing orbits in the n-body problem with simple choreography constraint
• On weak KAM theory for N-body problems

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• On weak KAM theory for N-body problems
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• Periodic solutions to a forced Kepler problem in the plane
• Busseman functions for the N-body problem
• Whiskered parabolic tori in the planar $(n+1)$-body problem
• Parabolic solutions for the planar $N$-centre problem: multiplicity and scattering
• Generic uniqueness of the minimal Moulton central configuration
• Parabolic orbits in Celestial Mechanics: a functional-analytic approach
• Minimizing configurations and Hamilton-Jacobi equations of homogeneous N-body problems
• Uniqueness of hyperbolic Busemann functions in the Newtonian N-body problem
• Existence of multisoliton solutions of the gravitational Hartree equation in three dimensions