论文标题
最小碰撞弧渐近到中心配置
Minimal collision arcs asymptotic to central configurations
论文作者
论文摘要
我们关注的是对一类奇异型均质$-α$的有限时间碰撞轨迹的分析，其中$-α$，$α\ in（0,2）$及其低阶扰动。众所周知，在合理的通用假设下，渐近归一化构型会收敛到中心配置。使用McGehee坐标，可以将流程扩展到具有中央配置作为固定点的碰撞歧管，并具有其稳定且不稳定的歧管。当渐近中心配置是球体上电势的全局最小化器时，我们关注的案例：我们的主要目标是在相当通用的环境中，局部稳定的歧管与最小碰撞弧的初始数据相吻合。这种表征在用破裂的测地构方法构建复杂轨迹时可能非常有用。证明利用了广义的Sundman的单调性公式。
We are concerned with the analysis of finite time collision trajectories for a class of singular anisotropic homogeneous potentials of degree $-α$, with $α\in(0,2)$ and their lower order perturbations. It is well known that, under reasonable generic assumptions, the asymptotic normalized configuration converges to a central configuration. Using McGehee coordinates, the flow can be extended to the collision manifold having central configurations as stationary points, endowed with their stable and unstable manifolds. We focus on the case when the asymptotic central configuration is a global minimizer of the potential on the sphere: our main goal is to show that, in a rather general setting, the local stable manifold coincides with that of the initial data of minimal collision arcs. This characterisation may be extremely useful in building complex trajectories with a broken geodesic method. The proof takes advantage of the generalised Sundman's monotonicity formula.
