The validity of the continuum limit in the gravitational N-body problem

Abstract

This paper attempts to give quantitative as well as qualitative answers to the question of the analogy between smooth potentials and N-body systems. A number of simulations were performed in both integrable and nonintegrable smooth environments and their frozen N-body analogues, and comparisons were made using a number of different tools. The comparisons took place on both statistical and pointwise levels. The results of this study suggest that microscopic chaos associated with discreteness effects is always present in N-body configurations. This chaos is different from the macroscopic chaos which is associated with the bulk potential and persists even for very large N. Although the Lyapunov exponents of orbits evolving in N-body environments do not decrease as N increases, comparisons associated with the statistical properties, as well as with the power spectra of the orbits, affirm the existence of the continuum limit.