In this paper, we study the limit behavior of a family of chords on compact energy hypersurfaces of a family of Hamiltonians. Under the assumption that the energy hypersurfaces are all of contact type, we give results on the Omega limit set of this family of chords. Roughly speaking, such a family must either end in a degeneracy, in which case it joins another family, or can be continued. This gives a Floer theoretic explanation of the behavior of certain families of symmetric periodic orbits in many well-known problems, including the restricted three-body problem.

中文翻译：

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和弦族的欧米茄极限集

在本文中，我们研究了一个弦族在哈密顿族的紧凑能量超曲面上的极限行为。在能量超曲面都是接触类型的假设下，我们给出了这个弦族的 Omega 极限集的结果。粗略地说，这样一个家庭必须要么以退化结束，在这种情况下它加入另一个家庭，要么可以继续存在。这给出了 Floer 理论解释某些对称周期轨道族在许多众所周知的问题中的行为，包括受限三体问题。