  This paper summarises an investigation of the effects of low amplitude noise
and periodic driving on phase space transport in 3-D Hamiltonian systems, a
problem directly applicable to systems like galaxies, where such perturbations
reflect internal irregularities and.or a surrounding environment. A new
diagnsotic tool is exploited to quantify how, over long times, different
segments of the same chaotic orbit can exhibit very different amounts of chaos.
First passage time experiments are used to study how small perturbations of an
individual orbit can dramatically accelerate phase space transport, allowing
`sticky' chaotic orbits trapped near regular islands to become unstuck on
suprisingly short time scales. Small perturbations are also studied in the
context of orbit ensembles with the aim of understanding how such
irregularities can increase the efficacy of chaotic mixing. For both noise and
periodic driving, the effect of the perturbation scales roughly in amplitude.
For white noise, the details are unimportant: additive and multiplicative noise
tend to have similar effects and the presence or absence of a friction related
to the noise by a Fluctuation- Dissipation Theorem is largely irrelevant.
Allowing for coloured noise can significantly decrease the efficacy of the
perturbation, but only when the autocorrelation time, which vanishes for white
noise, becomes so large that t here is little power at frequencies comparable
to the natural frequencies of the unperturbed orbit. This suggests strongly
that noise-induced extrinsic diffusion, like modulational diffusion associated
with periodic driving, is a resonance phenomenon. Potential implications for
galaxies are discussed.
