Abstract
Box orbits in triaxial potentials are generically thin, that is, they lie close in phase space to a resonant orbit satisfying a relation of the form lω1 + mω2 + nω3 = 0 between the three fundamental frequencies. Resonant orbits are confined for all time to a membrane in configuration space; they play roughly the same role in structuring the phase space of three-dimensional systems that periodic orbits play in two dimensions. Stable resonant orbits avoid the center of the potential; orbits that are thick enough to pass near the destabilizing center are typically stochastic. Resonances in triaxial potentials are most important at energies far outside the region of gravitational influence of a central black hole. Near the black hole, the motion is essentially regular, although resonant orbits exist in this region as well, including at least one family whose elongation is parallel to the long axes of the triaxial figure.
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