DIFFUSIVE TRANSPORT ENHANCEMENT AND ESCAPE PROCESSES IN FRICTIONLESS NONLINEAR OSCILLATORS WITH NOISE

The time-dependent escape rates and evolution of a distribution densit y are considered for a Hamiltonian many-dimensional nonlinear oscillat or with external noise. The Hamiltonian dynamics is assumed to be near ly integrable and is angle described in terms of isolated nonlinear re sonances. In case of a small angle between the resonant oscillations a nd the resonance line, a dynamic enhancement of diffusion occurs insid e the separatrix, leading to a strongly enhanced growth of distributio n tails and escape rates even when the resonances are relatively narow . The underlying mechanism of the phenomenon is essentially many-dimen sional.