The manifold structure for collision and for hyperbolic-parabolic orbits in the n-body problem (Q1061515)

(From author's introduction) The purpose of this paper is to analyze collision and parabolic orbits of Newtonian n-body systems. (What constitutes a collision orbit is self-explanatory. Parabolic motion is a transition motion for escape orbits where the escape velocity approaches zero as time approaches infinity.) In particular we will be interested in the structure of C, the set of initial conditions whose solutions terminate in a collision singularity, and P, the set of initial conditions whose solutions have at least two particles which define a parabolic orbit. Furthermore, we will analyze the asymptotic properties of collision and parabolic orbits as well as the complex analytic classification of a collision singularity. This last issue relates to whether or not a collision singularity can be removed. Some of the techniques in this paper rely upon an earlier study [the author and \textit{N. D. Hulkower}, ibid. 41, 27-43 (1981; Zbl 0475.70010)], where several of the issues concerning the asymptotic behavior of orbits were considered and resolved for the special cases of total collapses and completely parabolic orbits of the n-body problem. The results in this current paper include all known cases of collisions and extend some of the results in the above paper.