  We use Laskar's frequency mapping technique to study the dynamics of triaxial
galaxies with central density cusps and nuclear black holes. For ensembles of
10^4 orbits, we numerically compute the three fundamental frequencies of the
motion, allowing us to map out the Arnold web. We also compute diffusion rates
of stochastic orbits in frequency space. The objects of fundamental importance
in structuring phase space are found to be the 3-dimensional resonant tori;
even when stable, such tori are not necessarily associated with periodic orbits
as in systems with only two degrees of freedom. Boxlike orbits are generically
stochastic, but some tube orbits are stochastic as well. The spectrum of
diffusion rates for box-like orbits at a given energy is well approximated as a
power law over at least six decades. Models with high central concentrations --
steep central cusps or massive black holes -- exhibit the most stochasticity. A
black hole with a mass of 0.3% the mass of the galaxy is as effective as the
steepest central density cusp at inducing stochastic diffusion. There is a
transition to global stochasticity in box-like phase space when the mass of a
central black hole exceeds 2% the galaxy mass. We predict a greater average
degree of dynamical evolution in faint ellipticals, due to their high central
densities and short crossing times. The evolution time is estimated to be
shorter than a galaxy lifetime for absolute magnitudes fainter than about -19
or -20, consistent with the observed change in many elliptical galaxy
properties at this luminosity.
