Nevanlinna Pick interpolation of attractors

A Nevanlinna–Pick algorithm is developed and applied to short numerical time series approximating trajectories of ordinary differential equations to determine whether the data are near the global attractor. The algorithm, while ultimately unstable to numerical error, is found to give reliable results for more data points than standard algorithms commonly used today. Connections between the growth of trajectories backward in time and the success in locating the global attractor are explored. The numerical sensitivity to both round-off errors and the integrator used to generate the time series is analysed. Applications are made to the Lorenz system and Kuramoto–Sivashinsky equation.