[1] A. Albouy et A. Chenciner, Le probl`eme des n corps et les distances mutuelles, Invent. Math. 131 (1998), 151-184.

[2] A. Chenciner et N. Desolneux, Minima de l'int´egrale d'action et ´equilibres relatifs de n corps, C.R.A.S. 326 S´erie I (1998), 1209-1212, and 327 S´erie I (1998), 193.

[3] A. Chenciner et A. Venturelli, Minima de l'int´egrale d'action du probl`eme newtonien de 4 corps de masses ´egales dans R3: orbites “hip-hop”, Celestial Mechanics, to appear.

[4] W. B. Gordon, A minimizing property of Keplerian orbits, Amer. J. Math. 99 (1970), 961-971.

[5] W. Y. Hsiang, Geometric study of the three-body problem, I, CPAM-620, Center for Pure and Applied Mathematics, University of California, Berkeley (1994). * This is particularly interesting because very few stable periodic orbits in the inertial frame are known for the three-body problem with equal masses. One example is Schubart's collinear orbit: Nulerische Aufsuchung periodischer Lo¨sungen im Dreiko¨rperproblem, Astronomische Nachriften vol. 283, pp. 17-22, 1956 (thanks to C. Simo´ for this reference). One fourth of this orbit travels collinearly from E3 to C1. The “eight” has strong similarities with the critical point which would result from Schubart's orbit by permuting the colliding bodies at each collision so that the result travels completely around the equator in the shape sphere. Another example is that of orbits periodic in a rotating frame in case of resonance. To this category belong the tight binary solutions with a third mass far away and the family of “interplay” solutions connecting them to Shubart's orbit (see M. H´enon, A family of periodic solutions of the planar three-body problem, and their stability, Celestial Mechanics 13, pp. 267-285, 1976 and the references there to papers by R. Broucke and J. D. Hadjidemetriou).

[6] R. Moeckel, Some qualitative features of the three-body problem, Contemp. Math. 81(1988), 1-21.

[7] R. Montgomery, The N-body problem, the braid group, and action-minimizing periodic solutions, Nonlinearity 11 (1998), 363-376.

[8] , Figure 8s with three bodies, preprint, August 1999.

[9] , The geometric phase of the three-body problem, Nonlinearity 9 (1996), 1341-

[10] C. Moore, Braids in Classical Gravity, Phys. Rev. Lett. 70 (1993), 3675-3679.

[11] K.-C. Chen, On Chenciner-Montgomery's orbit in the three-body problem, Discrete and Continuous Dynamical Systems, to appear.