论文标题
$ n $ body问题的地球射线
Geodesic rays of the $N$-body problem
论文作者
论文摘要
对于牛顿n体问题，我们研究了非负能级的雅各比·莫普尔图斯度量。我们表明，大地射线是膨胀的，也就是说，身体之间的所有距离都必须是不同的功能。更确切地说，我们证明，这种运动的演变渐近地分解为完全抛物线膨胀的自由颗粒和子系统。该定理特别适用于固定的汉密尔顿 - 雅各比方程$ h（x，d_xu）= h $的任何给定的全局粘度解的最大特性曲线。
For the Newtonian N-body problem, we study the Jacobi-Maupertuis metric of the nonnegative energy levels. We show that the geodesic rays are expansive, that is to say, all the distances between the bodies must be divergent functions. More precisely, we prove that the evolution of such motions asymptotically decomposes into free particles and subsystems in completely parabolic expansion. The theorem applies in particular to the maximal characteristic curves of any given global viscosity solution of the stationary Hamilton-Jacobi equation $H(x,d_xu) = h$.
