Smooth potential chaos and N-body simulations

Integrations in fixed N-body realisations of smooth density distributions corresponding to a chaotic galactic potential can be used to derive reliable estimates of the largest (finite time) Lyapunov exponent X_S associated with an orbit in the smooth potential generated from the same initial condition, even though the N-body orbit is typically characterised by an N-body exponent X_N >> X_S. This can be accomplished either by comparing initially nearby orbits in a single N-body system or by tracking orbits with the same initial condition evolved in two different N-body realisations of the same smooth density.