Four Open Questions for the N-Body Problem

Part I. Tour, Problem, and Structures: -1. A tour of solutions; 0. The problem and its structure; Part II. The Questions: 1. Are the central configurations finite?; 2. Are there any stable periodic orbits?; 3. Is every braid realized?; 4. Does a scattered beam have a dense image?; Appendices: A. Geometric mechanics; B. Reduction and Poisson brackets; C. The three-body problem and the shape sphere; D. The orthogonal group and its Lie algebra; E. Braids, homotopy and homology; F. The Jacobi-Maupertuis metric; G. Regularizing binary collisions; H. One-degree of freedom and central scattering; References; Index.

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