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

Alain Chenciner (1)

1 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides

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.

Domaines: Systèmes dynamiques [math.DS]

Alain Chenciner. Action minimizing solutions of the Newtonian n-body problem: from homology to symmetry. Proceedings of the ICM, Beijing 2002, 2002, 3, pp.255-264. ⟨hal-00145797⟩