论文标题
关于牛顿重力系统的大地射线
On Geodesic Rays of Newtonian Gravitational Systems
论文作者
论文摘要
在本文中，我们专注于牛顿n体问题的一组大地测量射线。我们发现，测量光线的极限也是地球射线，因此它们在初始条件的空间中并不致密。结果，有许多动作的域是一半真实线的总能量，并且不是地球射线，而这种动作的集合具有积极的措施，我们认为这套设置提供了很大的空间来适应许多具有“不良”行为的解决方案。作为弱KAM理论在N体问题中的应用，我们简要证明了从任何给定的初始位置开始的完全抛物线轨道的存在。
In this paper, we focus on the set of geodesics rays of the Newtonian N-body problem. We find that the limits of geodesic rays are also geodesic rays, hence they are not dense in the space of initial conditions. As a result, there are many motions whose domain is the half real line has non-negative total energy, and they are not geodesic rays, the set of such motions has positive measure, we think this set gives a large space to accommodate many solutions with "bad" behaviors. As an application of weak KAM theory for N-body problem, we give a brief proof of the existence of complete parabolic orbit starting from any given initial position.
