论文标题
在受限的三体问题中
Pseudo-holomorphic dynamics in the restricted three-body problem
论文作者
论文摘要
在本文中，我们确定了Hofer-Wysocki-Zhhnder引入的有限能量叶面的5维类似物，用于研究三维REEB流量，并在平面动力学是CONVEX时，证明了这些空间循环限制的三体问题（SCR3BP）存在于空间循环限制的三体问题（SCR3BP）。我们介绍了纤维旋转点的概念，这可能被认为是Moser引入的叶轮交叉点的象征性版本，并表明它们在SCR3BP中的扰动状态中存在丰富。然后，我们使用这种叶子来通过使用伪形曲线来诱导标准3-sphere上的REEB流，被理解为保留叶面的给定动力学的最佳近似。我们讨论示例，进一步的几何结构，并推测可能的应用。
In this article, we identify the 5-dimensional analogue of the finite energy foliations introduced by Hofer--Wysocki--Zehnder for the study of 3-dimensional Reeb flows, and show that these exist for the spatial circular restricted three-body problem (SCR3BP) whenever the planar dynamics is convex. We introduce the notion of a fiberwise-recurrent point, which may be thought of as a symplectic version of the leafwise intersections introduced by Moser, and show that they exist in abundance for a perturbative regime in the SCR3BP. We then use this foliation to induce a Reeb flow on the standard 3-sphere, via the use of pseudo-holomorphic curves, to be understood as the best approximation of the given dynamics that preserves the foliation. We discuss examples, further geometric structures, and speculate on possible applications.
