Journal of Statistical Physics, Vol. 72, Nos. 3/4, 1993. p. 555-570.
The time-dependent escape rates and evolution of a distribution density are considered for a Hamiltonian many-dimensional nonlinear oscillator with external noise. The Hamiltonian dynamics is assumed to be nearly integrable and is described in terms of isolated nonlinear resonances. In case of a small angle between the resonant oscillations and the resonance line, a dynamic enhancement of diffusion occurs inside the separatrix, leading to a strongly enhanced growth of distribution tails and escape rates even when the resonances are relatively narow. The underlying mechanism of the phenomenon is essentially many-dimensional.