We prove the existence of periodic solutions of the N = (n + 1)-body problem starting with n bodies whose reduced motion is close to a non-degenerate central configuration and replacing one of them by the center of mass of a pair of bodies rotating uniformly. When the motion takes place in the standard Euclidean plane, these solutions are a special type of braid solutions obtained numerically by C Moore. The proof uses blow-up techniques to separate the problem into the n-body problem, the Kepler problem, and a coupling which is small if the distance of the pair is small. The formulation is variational and the result is obtained by applying a Lyapunov–Schmidt reduction and by using the equivariant Lyusternik–Schnirelmann category.

我们证明了N = ( n + 1)-body 问题的周期解的存在性，从n 个物体开始，这些物体的减少运动接近于非退化中心配置，并用一对物体的质心替换其中一个匀速旋转。当运动发生在标准欧几里得平面上时，这些解是 C Moore 数值获得的一种特殊类型的辫子解。证明使用了吹胀技术将问题分为n体问题、开普勒问题和耦合（如果对的距离很小，则耦合也很小）。该公式是变分的，结果是通过应用 Lyapunov-Schmidt 约简和使用等变 Lyusternik-Schnirelmann 类别获得的。