论文标题
累积中心和循环和椭圆限制的三体问题的广义周期性轨道
Generalized Periodic Orbits of Time-Periodically Forced Kepler Problem Accumulating the Center and of Circular and Elliptic Restricted Three-Body Problems
论文作者
论文摘要
在本文中，我们考虑了任何维度的时间周期性强迫开普勒问题，外部力量我们只假定在有吸引力的中心附近是规律的。我们证明，该系统中存在无限的周期轨道，并可能与中心正规化的双重碰撞，从而积累了有吸引力的中心。结果是通过本地化参数与$ c^{1} $的结果相结合的 - 通过本地同型旋转参数对封闭轨道的持久性的结果。因此，通过将任何维度的循环和椭圆形限制的三体问题作为时间周期性强迫开普勒问题，我们获得了无限的多个周期轨道，可能会与原始人正式化的双重碰撞，并积聚在每个初处。
In this paper, we consider a time-periodically forced Kepler problem in any dimensions, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic orbits in this system, with possible double collisions with the center regularized, which accumulate the attractive center. The result is obtained via a localization argument combined with a result on $C^{1}$-persistence of closed orbits by a local homotopy-streching argument. Consequently, by formulating the circular and elliptic restricted three-body problems of any dimensions as time-periodically forced Kepler problems, we obtain that there exists infinitely many periodic orbits, with possible double collisions with the primaries regularized, accumulating to each of the primaries.
