Based on quantitative “kam theory”, we state and prove two theorems about the continuation of maximal and whiskered quasi-periodic motions to slightly perturbed systems exhibiting proper degeneracy. Next, we apply such results to prove that, in the three-body problem, there is a small set in phase space where it is possible to detect both such families of tori. We also estimate the density of such motions in proper ambient spaces. Up to our knowledge, this is the first proof of co-existence of stable and whiskered tori in a physical system.

中文翻译：

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定量 kam 理论及其在三体问题中的应用

基于定量的“ kam理论”，我们陈述并证明了关于最大和晶须准周期运动对于表现出适当简并性的轻微扰动系统的连续性的两个定理。接下来，我们应用这些结果来证明，在三体问题中，相空间中存在一个小集合，可以在其中检测到这两个环面族。我们还估计了适当的周围空间中此类运动的密度。据我们所知，这是稳定和须状环面在物理系统中共存的第一个证据。