SLOW CROSSING OF A STOCHASTIC LAYER

The extension of the adiabatic invariant theory to separatrix crossing has led to a good understanding of the captures into resonance modell ized by a slowly varying one-degree-of-freedom Hamiltonian system. How ever. in many applications the one degree of freedom system considered is only an approximation of a system with more degrees of freedom and one must consider that the separatrix is actually a stochastic layer. In an earlier paper, such a situation was investigated and an asympto tic approximation was developed. Numerical experiments confirmed this asymptotic approximation but only for very slow rates of evolution, mu ch slower than expected. We identify here the reason for this behavior , the smallness of the diffusion coefficient in the stochastic layer.