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.