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

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

2003-04-28

arxiv.org/abs/math/0304449v1

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

Mathematics

Dynamical Systems

Scientific paper

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.

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