In scale-free models the allowed orbits are more complex, and it's not clear if such models can be in true equilibrium. The last step is the most difficult. In general Eq. 9 has many solutions, reflecting the fact that many different distribution functions are consistent with a given mass model. Apart from the choice of streaming motion, thin tube models are unique . Each boxlet family is associated with a closed and stable orbit arising from a resonance between the motions in the x and y directions.
Similar results hold for scale-free models in three dimensions.
A few models have been constructed using Schwarzschild's method, but little is known about the existence and stability of such systems. N-body experiments indicate that at least some such systems are viable models of elliptical galaxies. Rotation tends to steer orbits away from the center and so may lessen the effects of central density cusps. Realistic potentials are likely to have some irregular or chaotic orbits, and there is no reason to think that such orbits are systematically avoided by processes of galaxy formation. Dejonghe, H. 1986, Phys.