Wavelet based time-frequency analysis for phase space structure and transport

Luz Vianey Vela-Arevalo, Center for Nonlinear Science, School of Physics, Georgia Institute of Technology

The method of time-frequency analysis based on wavelets consists of assigning time varying frequencies to the numerically computed trajectories of dynamical systems. Since regular trajectories have constant frequencies, the time variation of the frequencies is a good indicator of chaos. The determination of time varying frequencies allows to identify quasiperiodic and resonant motion; and provides a good description of the transport properties of chaotic trajectories. The method extends naturally for higher dimensional systems. In this talk, the application of the method to several problems will be described.