Time–frequency analysis of chaotic systems

We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time–frequency decomposition of a trajectory using wavelets. The ridges of the time–frequency landscape of a trajectory, also called instantaneous frequencies, enable us to analyze the phase space structures. In particular, this method detects resonance trappings and transitions and allows a characterization of the notion of weak and strong chaos. We illustrate the method with the trajectories of the standard map and the hydrogen atom in crossed magnetic and elliptically polarized microwave fields.