The existence of rotating accelerator-mode islands (RAIs), performing quasiregular motion in rotational resonances of order $m>1$ of the standard map, is firmly established by an accurate numerical analysis of all the known data. It is found that many accelerator-mode islands for relatively small nonintegrability parameter $K$ are RAIs visiting resonances of different orders $m⩽3$. For sufficiently large $K$, one finds also “pure” RAIs visiting only resonances of the same order, $m=2$ or $m=3$. RAIs, even quite small ones, are shown to exhibit sufficient stickiness to produce an anomalous chaotic transport. The RAIs are basically different in nature from accelerator-mode islands in resonances of the “forced” standard map which was extensively studied recently in the context of quantum accelerator modes.

• Received 22 December 2006

DOI:https://doi.org/10.1103/PhysRevE.75.056209