  The long therm behavior of chaotic flows is investigated by means of time
dependent frequency analysis. The system under test consists of an electrically
conducting fluid, confined between two differentially rotating spheres. The
spherical setup is exposed to an axial magnetic field. The classical Fourier
Transform method provides a first estimation of the time dependence of the
frequencies associated to the flow, as well as its volume-averaged properties.
It is however unable to detect strange attractors close to regular solutions in
the Feigenbaum as well as Newhouse-Ruelle-Takens bifurcation scenarios. It is
shown that Laskar's frequency algorithm is sufficiently accurate to identify
these strange attractors and thus is an efficient tool for classification of
chaotic flows in high dimensional dynamical systems. Our analysis of several
chaotic solutions, obtained at different magnetic field strengths, reveals a
strong robustness of the main frequency of the flow. This frequency is
associated to an azimuthal drift and it is very close to the frequency of the
underlying unstable rotating wave. In contrast, the main frequency of
volume-averaged properties can vary almost one order of magnitude as the
magnetic forcing is decreased. We conclude that, at the moderate differential
rotation considered, unstable rotating waves provide a good description of the
variation of the main time scale of any flow with respective variations in the
magnetic field.
