Global superdiffusion of weak chaos

A class of kicked rotors is introduced, exhibiting accelerator-mode islands (AIs) and global superdiffusion for arbitrarily weak chaos. The corresponding standard maps are shown to be exactly related to generalized web maps taken modulo an “oblique cylinder.” Then, in a case that the web-map orbit structure is periodic in the phase plane, the AIs are essentially normal web islands folded back into the cylinder. As a consequence, chaotic orbits sticking around the AI boundary are accelerated only when they traverse tiny “acceleration spots.” This leads to chaotic flights having a quasiregular steplike structure. The global weak-chaos superdiffusion is thus basically different in nature from the strong-chaos one in the usual standard and web maps.