Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of quasi periodic motions in phase space is studied via the Hamilton-Jacobi equation. The main result, a high density theorem of invariant tori, is derived by the classical canonical transformation method extending previous results. As an application the existence of long heteroclinic chains (and of Arnol'd diffusion) is proved for systems interacting through a trigonometric polynomial in the angle variables.
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机译：在非耦合系统具有三个截然不同的特征时间尺度的情况下，考虑了由两个旋转器和一个靠近双曲不动点的点质量组成的相互作用系统。通过汉密尔顿-雅可比方程研究了相空间中准周期运动的丰度.主要结果是不变 tori 的高密度定理，通过扩展先前结果的经典正则变换方法推导而来。作为一种应用，对于通过角度变量中的三角多项式相互作用的系统，证明了长异斜链（和 Arnol'd 扩散）的存在。
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