On time-dependent orbital complexity in gravitational N-body simulations

We implement an efficient method to quantify time-dependent orbital complexity in gravitational N-body simulations. The technique, which we name DWaTIM, is based on a discrete wavelet transform of velocity orbital time-series. The wavelet power spectrum is used to measure trends in complexity continuously in time. We apply the method to the test cases N= 3 Pythagorean configuration and a perturbed N= 5 Caledonian configuration. The method recovers the well-known time-dependent complexity of the dynamics in these small-N problems. We then apply the technique to an equal-mass collisional N= 256 body simulation run through core-collapse. We find that a majority of stars evolve on relatively complex orbits up to the time when the first hard binary forms, whereas after core-collapse, less complex orbits are found on the whole as a result of expanding mass shells.