Results of systematic numerical explorations of local scaling of the flux near a critical invariant circle for a class of standardlike maps are reported. The scaling law is universal and the universality class is determined apparently only by the tail in the rotation number of the critical invariant circle. The flux near just created cantori is also studied, and another type of scaling is indicated, which is a combination of the scaling laws in the critical and the strongly supercritical regimes.

• Received 5 April 2002

DOI:https://doi.org/10.1103/PhysRevE.66.046221