, Volume 20, Issue 1, pp 59-72

On the integral manifolds of theN-body problem

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Abstract

Here we make a topological study of the mapI=(E, J), whereE is the energy andJ is the angular momentum of then-body problem in 3-space. Part of the bifurcation set ofI is characterized and some topological information is given on the integral manifolds of negative energy and zero angular momentum.

This paper is the author's doctoral dissertation prepared under the supervision of Professor S. Smale at the University of California, Berkeley. Part of this work was done during a 3 months visit at the Institut des Hautes Etudes Scientifiques.