The search for the lost attractor

Abstract

N-body systems characterized by inverse square attractive forces may display a self similar collapse known as the gravo-thermal catastrophe. In star clusters, collapse is halted by binary stars, and a large fraction of Milky Way clusters may have already reached this phase. It has been speculated -- with guidance from simulations -- that macroscopic variables such as central density and velocity dispersion are governed post-collapse by an effective, low-dimensional system of ODEs. It is still hard to distinguish chaotic, low dimensional motion, from high dimensional stochastic noise. Here we apply three machine learning tools to state-of-the-art dynamical simulations to constrain the post collapse dynamics: topological data analysis (TDA) on a lag embedding of the relevant time series, Sparse Identification of Nonlinear Dynamics (SINDY), and Tests of Accuracy with Random Points (TARP).