Identification of gravitational wave signals from chaotic astrophysical systems through phase space and attractor properties

Phase space and attractor dimensions in a gravitational wave detector output can be estimated in order to identify chaotic (deterministic) signals in the presence of additive Gaussian noise. These quantities are evaluated, respectively, by means of conditional probabilities and the Grassberger-Procaccia algorithm, both methods relying on embedding in a suitable space of dimension d. By testing with different embedding dimensions, a deterministic—though erratic—signal can be detected by comparing the corresponding conditional probabilities via Kolmogorov-Smirnoff test and checking whether the correlation (fractal) dimension differs from d. Results of the two approaches are eventually compared, both for chaotic and periodic trajectories.