N-body models

The experimental discovery of an overstability in the central regions of galaxies is briefly discussed, and numerical methods for integrating orbits are briefly addressed. The overstability manifests itself as a growing amplitude in the orbit of a galaxy's nucleus about its mass centroid. This finding may complicate studies of the topological properties of orbits and studies of the bifurcation structure of orbits. A sample problem is used to illustrate the importance of a Liouville theorem in N-body calculations.