We use numerical simulations to study the evolution of triaxial elliptical
galaxies with central black holes. In contrast to earlier numerical studies
which used galaxy models with central density ``cores,'' our galaxies have
steep central cusps, like those observed in real ellipticals. As a black hole
grows in these cuspy triaxial galaxies, the inner regions become rounder owing
to chaos induced in the orbit families which populate the model. At larger
radii, however, the models maintain their triaxiality, and orbital analyses
show that centrophilic orbits there resist stochasticity over many dynamical
times. While black hole induced evolution is strong in the inner regions of
these galaxies, and reaches out beyond the nominal ``sphere of influence'' of a
black hole, our simulations do not show evidence for a rapid {\it global}
transformation of the host. The triaxiality of observed elliptical galaxies is
therefore not inconsistent with the presence of supermassive black holes at
their centers.Comment: 15 pages, 7 figures (1 color). Accepted for publication in Ap