Orbits in Adiabatically Contracting Spherical Potentials

Abstract
It was recently shown in N-body simulations that the simple adiabatic invariant r M(r) describes the evolution of a contracting spherical density distribution very well. This is surprising as this adiabatic invariant is only valid for circular orbits. Orbits in spherically symmetric potentials resemble rather precessing ellipses. We want to highlight some problems involved in proving the validity of the adiabatic approximation on a orbit to orbit basis. Statistical methods are more promising.