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 x0, there exists a collision-free parabolic solution starting from x i and asymptotic to x0. 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 x0.
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Communicated by P. Rabinowitz
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Maderna, E., Venturelli, A. Globally Minimizing Parabolic Motions in the Newtonian N-body Problem. Arch Rational Mech Anal 194, 283–313 (2009). https://doi.org/10.1007/s00205-008-0175-8
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DOI: https://doi.org/10.1007/s00205-008-0175-8