  We investigate the timescales for stochasticity and chaotic mixing in a
family of triaxial potentials that mimic the distribution of light in
elliptical galaxies. Some of the models include central point masses designed
to represent nuclear black holes. Most of the boxlike orbits are found to be
stochastic, with mean Liapunov times that are 3-6 times the period of the
long-axis orbit. In models with large cores or small black holes, the
stochastic orbits mimic regular box orbits for hundreds of oscillations at
least. However a small core radius or significant black hole mass causes most
of the stochastic orbits to diffuse through phase space on the same timescale,
visiting a significant fraction of the volume beneath the equipotential
surface. We estimate timescales for chaotic mixing in the more strongly
stochastic models by evolving ensembles of 10^4 points until their distribution
reaches a nearly steady state. Mixing initially takes place rapidly, with
characteristic times of 10-30 dynamical times, as the phase points fill a
region similar in shape to that of a box orbit. Subsequent mixing is slower,
with characteristic times of hundreds of orbital times. Mixing rates were found
to be enhanced by the addition of modest force perturbations. The consequences
for the structure and evolution of elliptical galaxies are discussed.
