限制性三体问题的接触几何

Existence of either a periodic collisional orbit or infinitely many consecutive collision orbits in the planar circular restricted three-body problem

In the restricted three-body problem, consecutive collision orbits are those orbits which start and end at collisions with one of the primaries. Interests for such orbits arise not only from mathematics but also from various engineering problems. In this article, using Floer homology, we show that there are either a periodic collisional orbit, or infinitely many consecutive collision orbits in the planar circular restricted three-body problem on each bounded component of the energy hypersurface for Jacobi energy below the first critical value.

$J^+$-like invariants of periodic orbits of the second kind in the restricted three body problem

We determine three invariants: Arnold's $J^+$-invariant as well as $\mathcal{J}_1$ and $\mathcal{J}_2$ invariants, which were introduced by Cieliebak-Frauenfelder-van Koert, of periodic orbits of the second kind near the heavier primary in the restricted three-body problem, provided that the mass ratio is sufficiently small.

具有限制切触型边界流形的弗洛尔同调中的Kunneth公式

The Kunneth formula in Floer homology for manifolds with restricted contact type boundary

证明了具有限制切触型边界的流形的Floer（余）同调的Kunneth公式.我们使用Viterbo的定义的弗洛尔同调，涉及辛完成添加一个积极的锥的边界。Kunneth公式包含了亚临界Stein流形的Floer（上）同调的消失。其他应用包括Weinstein猜想在某些产品流形，障碍，以确切的拉格朗日嵌入，存在的全纯曲线与拉格朗日边界条件，以及辛容量。

计算辛拓扑与限制性三体问题中的对称轨道

Computational symplectic topology and symmetric orbits in the restricted three-body problem

本文提出计算方法证明限制性三体问题的伯克霍夫猜想，通过验证数值技术证明广泛参数下近似圆形直接轨道存在，提供严格计算Conley-Zehnder指标的方法，为开发计算弗勒尔同调及证明猜想奠基，并应用于对称轨道。

平面限制性三体问题的整体截面曲面

Global surfaces of section in the planar restricted 3-body problem

限制性平面三体问题有着悠久的历史，但仍有许多未解之谜。在本文中，我们证明了存在一个全球性的表面附近的较小的机构在一个新的范围内的能量和质量比的希尔地区仍然有三个连通的组件。该方法依赖于最近的全球方法在辛几何和对比鲜明的微扰方法使用到现在。

Some remarks on symmetric periodic orbits in the restricted three-body problem

The planar circular restricted three body problem (PCRTBP) is symmetric with respect to the line of masses and there is a corresponding anti-symplectic involution on the cotangent bundle of the 2-sphere in the regularized PCRTBP. Recently it was shown that each bounded component of an energy hypersurface with low energy for the regularized PCRTBP is fiberwise starshaped. This enable us to define a Lagrangian Rabinowitz Floer homology which is related to periodic orbits symmetric for the anti-symplectic involution in the regularized PCRTBP and hence to symmetric periodic orbits in the unregular…

在第一临界能量值以上的限制性三体问题中的连续碰撞轨道

Consecutive collision orbits in the restricted three-body problem above the first critical energy value

本文研究能量水平略高于第一临界值的平面圆型限制性三体问题，利用 Rabinowitz Floer 同调证明了周期对称碰撞轨道或无穷多个对称连续碰撞轨道的存在性，并通过解析延拓论证得出至少存在两个对称连续碰撞轨道。

圆型限制性三体问题中的双法向轨迹

Bi-normal trajectories in the Circular Restricted Three-Body Problem

本文利用相对 Poincaré-Birkhoff 定理，证明了在特定能量与扭转条件下，空间圆型限制性三体问题中存在无穷多条双法向轨迹。