Chaos in Core Oscillations of Globular Clusters

We develop techniques with general applicability in searching for low dimensional chaotic behavior in non-uniformly sampled time series data. This is done through the analysis of a specific example, viz. post-collapse core oscillations in globular star cluster evolution. Using simulation data from a Fokker-Planck model that includes energy input from binaries formed in three-body interactions, we present evidence for a bifurcation sequence leading to a low dimensional chaotic attractor. We show state space portraits of the attractor reconstructed in three dimensions and calculate a correlation dimension for each. For every value of the total star number in the range $N_s \ge 1.5 \times 10^4$, we calculate a positive Lyapunov exponent, which suggests deterministic chaos.