We study solutions of the Newtonian $n$-body problem which tend to infinity hyperbolically, that is, all mutual distances tend to infinity with nonzero speed as $t \rightarrow +\infty$ or as $t \rightarrow -\infty$. In suitable coordinates, such solutions form the stable or unstable manifolds of normally hyperbolic equilibrium points in a boundary manifold "at infinity". We show that the flow near these manifolds can be analytically linearized and use this to give a new proof of Chazy's classical asymptotic formulas. We also address the scattering problem, namely, for solutions which are hyperbolic in both forward and backward time, how are the limiting equilibrium points related? After proving some basic theorems about this scattering relation, we use perturbations of our manifold at infinity to study scattering "near infinity", that is, when the bodies stay far apart and interact only weakly.

中文翻译：

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n体问题的Chazy型渐近和双曲散射

我们研究牛顿 $n$-body 问题的解决方案，该问题倾向于双曲线无穷大，即所有相互距离都趋于无穷大，速度为 $t \rightarrow +\infty$ 或 $t \rightarrow -\infty$。在合适的坐标中，这种解在“无穷远”边界流形中形成通常双曲平衡点的稳定或不稳定流形。我们表明这些流形附近的流动可以被分析线性化，并使用它来给出 Chazy 经典渐近公式的新证明。我们还解决了散射问题，即对于前向和后向双曲线的解，极限平衡点是如何相关的？在证明了关于这种散射关系的一些基本定理之后，我们使用我们的流形在无穷远处的扰动来研究散射“