On the sensitivity of the N-body problem to small changes in initial conditions. II

Abstract

Attention is given to the microscopic instability of the gravitational N-body problem toward small changes in initial conditions, with emphasis on the scale invariance of the nonlinear evolution of an initial perturbation, the effects of allowing for a system comprised of two mass species (m1 and m2 = 5m1), and possible differences arising for special initial conditions corresponding to a collisionless equilibrium. In a precise sense, scale invariance is found to obtain for simulations with an initial virial ratio Z0 = 1.0, which entail no systematic expansion or contraction. Allowing for two mass species is seen to introduce no systematic effects on short time scales of the order of the average e-folding time. This complication does have an effect at later times, at least for simulations with Q0 = 0.5, resulting in a systematic increase in the rate at which initial perturbations grow, and in differences in the behavior of the two mass components which correlate with the phenomenon of mass segregation.