通过在中心配置中布线的N体问题的辫子
Braids of the N-body problem by cabling a body in a central configuration
摘要：
我们证明了N=（n+1）-体问题周期解的存在性，其中n个物体的约化运动接近于一个非退化中心构型，用一对匀速转动物体的质心代替其中一个物体.当运动发生在标准欧几里德平面上时，这些解是C.摩尔证明使用爆破技术分离成n体问题的问题，开普勒问题，和耦合，这是小，如果对的距离是小的。该公式是变分的，其结果是通过应用Lyapunov-Schmidt约化和使用等变Lyusternik-Schnirelmann范畴得到的。
英文摘要：
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.
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