The Orbital Structure of Triaxial Galaxies with Figure Rotation
  We survey the properties of all orbit families in the rotating frame of a
family of realistic triaxial potentials with central supermassive black holes
(SMBHs). In such galaxies, most regular box orbits (vital for maintaining
triaxiality) are associated with resonances which occupy two-dimensional
surfaces in configuration space. For slow figure rotation all orbit families
are largely stable. At intermediate pattern speeds a significant fraction of
the resonant box orbits as well as inner long-axis tubes are destabilized by
the "envelope doubling" that arises from the Coriolis forces and are driven
into the destabilizing center. Thus, for pattern rotation periods .2 Gyr < Tp <
5 Gyr, the two orbit families that are most important for maintaining
triaxiality are highly chaotic. As pattern speed increases there is also a
sharp decrease in the overall fraction of prograde short-axis tubes and a
corresponding increase in the retrograde variety. At the highest pattern speeds
(close to that of triaxial bars), box-like orbits undergo a sudden transition
to a new family of stable retrograde loop-like orbits, which resemble orbits in
three-dimensional bars, and circulate about the short axis. Our analysis
implies that triaxial systems (with central cusps and SMBHs) can either have
high pattern speeds like fast bars or low patten speeds like triaxial
elliptical galaxies or dark matter halos found in N-body simulations.
Intermediate pattern speeds produce a high level of stochasticity in both the
box and inner long-axis tube orbit families implying that stable triaxial
systems are unlikely to have such pattern speeds.
