  ABBREVIATED ABSTRACT: This paper summarises an investigation of the effects
of weak friction and noise in time-independent, nonintegrable potentials which
admit both regular and stochastic orbits. The aim is to understand the
qualitative effects of internal and external irregularities associated, e.g.,
with discreteness effects or couplings to an external environment, which stars
in any real galaxy must experience. The two principal conclusions are: (1)
These irregularities can be important on time scales much shorter than the
natural relaxation time scale t_R associated with the friction and noise. For
stochastic orbits friction and noise induce an average exponential divergence
from the unperturbed Hamiltonian trajectory at a rate set by the value of the
local Lyapunov exponent. Even weak noise can make a pointwise interpretation of
orbits suspect already on time scales much shorter than t_R. (2) The friction
and noise can also have significant effects on the statistical properties of
ensembles of stochastic orbits, these also occurring on time scales much
shorter than t_R. Potential implications for galactic dynamics are discussed,
including the problem of shadowing.
