论文标题
固定点和中央配置的逆问题
Fixed points and the inverse problem for central configurations
论文作者
论文摘要
中心配置在$ n $ body问题的动力学中起着重要作用：它们是相对平衡的，在碰撞轨迹中以渐近配置的形式出现。我们说明了如何找到它们作为形状空间定义的自动图的投影固定点，以及在尺寸$ 1 $中的反问题上的一些结果，即发现（正或真实）质量，这些质量是给定的colinear配置中央的质量。这篇调查文章向读者介绍了作者的最新结果，也未发表，显示了固定点理论的应用。
Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed points of self-maps defined on the shape space, and some results on the inverse problem in dimension $1$, i.e. finding (positive or real) masses which make a given collinear configuration central. This survey article introduces readers to the recent results of the author, also unpublished, showing an application of the fixed point theory.
