  Figure rotation substantially increases the fraction of stochastic orbits in
triaxial systems. This increase is most dramatic in systems with shallow cusps
showing that it is not a direct consequence of scattering by a central density
cusp or black hole. In a recent study of stationary triaxial potentials
(Valluri & Merritt 1998) it was found that the most important elements that
define the structure of phase space are the two dimensional resonant tori. The
increase in the fraction of stochastic orbits in models with figure rotation is
a direct consequence of the destabilization of these resonant tori. The
presence of a large fraction of stochastic orbits in a triaxial bulge will
result in the evolution of its shape from triaxial to axisymmetric. The
timescales for evolution can be as short as a few crossing times in the bulges
of galaxies and evolution is accelerated by figure rotation. This suggests that
low luminosity ellipticals and the bulges of early type spirals are likely to
be predominantly axisymmetric.
