Orbital motion in triaxial nuclei with central point masses , representing supermassive black holes , is investigated .
The stellar density is assumed to follow a power law , \rho \propto r ^ { - \gamma } , with \gamma = 1 or \gamma = 2 .
At low energies the motion is essentially regular ; the major families of orbits are the tubes and the pyramids .
Pyramid orbits are similar to box orbits but have their major elongation parallel to the short axis of the figure .
A number of regular orbit families associated with resonances also exist , most prominently the banana orbits , which are also elongated parallel to the short axis .
At a radius where the enclosed stellar mass is a few times the black hole mass , the pyramid orbits become stochastic .
The energy of transition to this “ zone of chaos ” is computed as a function of \gamma and of the shape of the stellar figure ; it occurs at lower energies in more elongated potentials .
Our results suggest that supermassive black holes may place tight constraints on departures from axisymmetry in galactic nuclei , both by limiting the allowed shapes of regular orbits and by inducing chaos .