Chaos in three-body dynamics: Kolmogorov–Sinai entropy

An ensemble of Newtonian three-body models with close initial separations is investigated by following the evolution of a 'drop' in the homology map. The onset of chaos is revealed by the motion and the complex temporal deformation of the drop. In the state of advanced chaos, the drop spreads over almost the whole homology map, quite independently of its initial position on the map. A general quantitative measure of this process is the mean exponential rate of spreading, which bears resemblance to Kolmogorov–Sinai entropy; this is introduced and estimated in terms of the homology mapping. In a similar manner we also estimate the mean exponential rate of divergence of initially close-by trajectories. This is a close analogue to the Lyapunov exponent. These parameters measure two complementary aspects of dynamical instability, which is the basic mechanism of the onset of chaos.