We show that three families of relative periodic solutions bifurcate out of the Eight solution of the equal-mass 3-body problem : the planar Hénon family, the spatial Marchal P12 family and a new… (More)

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,… (More)

We study both theoretically and numerically the Lyapunov families which bifurcate in the vertical direction from a horizontal relative equilibrium in R. As explained in [CF1], very symmetric relative… (More)

From a normal form analysis near the Lagrange equilateral relative equilibrium, we deduce that, up to the action of similarities and time shifts, the only relative periodic solutions which bifurcate… (More)

Nevertheless, a 2 × 2 determinant would be less surprising* than a 4 × 4 determinant. What follows originates from work ([AC], see also [A3] and [C1]) done in collaboration with Alain Albouy on the… (More)

The simplest solutions of the N-body problem –symmetric relative equilibria– are shown to be organizing centers from which stem some recently studied classes of periodic solutions. We focus in… (More)

A section in the 2-jet space of Morse functions is not always homotopic to a holonomic section. We give a necessary condition for being the case and we discuss the sufficiency.