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We present the first self-consistent models of triaxial galaxies with central density cusps. The mass distribution is the triaxial generalization of the spherical ``eta'' models, $\rho \propto m^{\eta-3}(1+m)^{-1- \eta }$, $ m^{2} =\frac {x^{2}} {a^{2}} + \frac {y^{2}} {b^{2}}+ \frac {z^{2}} {c^{2}} $. The eta models look similar to a de Vaucouleurs profile in projection but have a central cusp with a power-law slope that can be adjusted from $0$ to $-2$. Here we present results for $\eta =1$, i.e. $\rho \propto r^{-2}$ near the center, similar to the observed luminosity density in M32. Most of the box orbits are unstable owing to the central singularity; they are replaced by stochastic orbits, which evolve strongly over a timescale of a few crossing times, and by some regular orbits associated with resonances. We discuss the constraints imposed by stochasticity on the shapes of triaxial models, and the likely importance of stochastic orbits in causing a slow evolution of elliptical galaxies.
