Rigidity of the anomalous transport of the standard map to time dependent perturbation

Superdiffusive anomalous transport in the standard map model can be especially strong for the cases of specially selected values of the control parameter, when a hierarchical set of islands has appeared. For these cases we introduce and study a notion of rigidity of the system with respect to a small periodic perturbation. It is shown that the kinetic properties of the system have a rigidity while the topology of the phase space is modified.