  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.
