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 χS 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 χN χS. 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.