Characterization of a periodically driven chaotic dynamical system

We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a local–in–time version of these quantities. In systems where the time scale related to the time periodic variation of the parameter is much larger than the ``internal’’ time scale, one has that the local quantities strongly depend on the phase of the cycle. In this case, the standard global quantities can give misleading information.