Regular and chaotic dynamics of triaxial stellar systems

We use Laskar's frequency mapping technique to study the dynamics of triaxi al galaxies with central density cusps and nuclear black holes. For ensembl es of similar to 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 object s of greatest importance in structuring phase space are found to be the thr ee-dimensional resonant tori, regions where the fundamental frequencies sat isfy a relation of the form 0 = l omega(1) + m omega(2) + n omega(3) with i nteger (l, m, n). When stable, resonant tori generate phase-space regions i n which the motion is regular; these regions are not necessarily associated with a stable periodic orbit as in systems with only 2 degrees of freedom. Boxlike orbits are generically stochastic, but some tube orbits are stocha stic as well. The spectrum of diffusion rates for boxlike orbits at a given energy is well approximated as a power law over at least 6 decades. Models with high central concentrations-steep central cusps or massive black hole s-exhibit the most stochasticity. Even a modest black hole, with a mass of similar to 0.5% the mass of the galaxy, is as effective as the steepest cen tral density cusp at inducing stochastic diffusion. There is a transition t o global stochasticity in boxlike phase space when the mass of the central black hole exceeds similar to 2% of the galaxy mass. We estimate the depend ence of orbital evolution rates on galaxy structural parameters. We predict a greater average degree of dynamical evolution in faint elliptical galaxi es because of their high central densities and short crossing times. The ev olution time is estimated to be shorter than a galaxy lifetime for absolute magnitudes fainter than about -19 or -20, consistent with the observed cha nge in many elliptical galaxy properties at this luminosity.