The present work studies the robustness of certain basic homoclinic motions in an equilateral restricted four-body problem. The problem can be viewed as a two-parameter family of conservative autonomous vector fields. The main tools are numerical continuation techniques for homoclinic and periodic orbits, as well as formal series methods for computing normal forms and center stable/unstable manifold parameterizations. After careful numerical study of a number of special cases, we formulate several conjectures about the global bifurcations of the homoclinic families.

中文翻译：

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受限四体问题中的临界同宿点：数值连续和中心流形计算

本工作研究在等边受限四体问题中某些基本同宿运动的鲁棒性。该问题可以看作是保守自主矢量场的两参数族。主要工具是用于单斜轨道和周期轨道的数值连续技术，以及用于计算法线形式和中心稳定/不稳定流形参数化的形式系列方法。在对一些特殊情况进行了仔细的数值研究之后，我们对同宿族的全球分叉提出了一些猜想。