Action minimizing solutions of the Newtonian n-body problem: from homology to symmetry

2003/04/28 by Alain Chenciner · 2 citations
Mathematics · #math.DS #msc:70F07 #msc:70F10 #msc:70F16 #msc:34C14 #msc:34C25

paper · pdf

published as Proceedings of the ICM, Beijing 2002, vol. 3, 255--264

arxiv created 2003/04/28 · arxiv updated 2009/11/30

Abstract

An action minimizing path between two given configurations, spatial or planar, of the n-body problem is always a true -- collision-free -- solution. Based on a remarkable idea of Christian Marchal, this theorem implies the existence of new "simple" symmetric periodic solutions, among which the Eight for 3 bodies, the Hip-Hop for 4 bodies and their generalizations.

Cited by

• On the regularity of solutions to the Hamilton-Jacobi equations for the N-body problem
• Positive energy solutions in the anisotropic Kepler problem with homogeneous potential

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