A signal processing method: detection of Lévy flights in chaotic trajectories

Abstract—Transport in low dimensional Hamiltonian chaos can be anomalous due to stickiness and rise of Lévy flights. We suggest a signal processing method to detect these flights in signals, in order to characterize the nature of transport (diffusive or anomalous). We use time-frequency techniques such as Fractional Fourier transform and matching pursuit in order to be robust to noise. The method is tested on data obtained from chaotic advection. I