Periodic Orbits in Triaxial Galaxies with Weak Cusps

The orbital structure of triaxial models with weak central density cusps, $\rho \propto r^{-\gamma },gamma<1$, is investigated. The stability of the $x$- (long-) axis orbit – and hence the existence of box orbits – depends sensitively on $\gamma$; the range of model shapes for which the $x$-axis orbit is stable becomes progressively smaller as $\gamma$ approaches one. The banana and fish boxlets in the $x-z$ (long axis-short axis) plane are stable over a wide range of model parameters. The boxlets in the $x-y$ and $y-z$ planes are generally vertically unstable.