Type specification of stability islands and chaotic stickiness

Abstract

A detailed characterization of stability islands in area-preserving maps is introduced on the basis of the resonance partition of phase space and it is used to define chaotic stickiness in these maps. It is shown that a general island can be characterized by a well-defined quasiregularity "type," specifying the sequence of resonances visited by the island. In particular, a "tangle" island lies entirely not just within the turnstile lobe of a resonance but also within the turnstile overlap of two resonances. Chaotic stickiness to a given island is then defined as the coincidence of the type of a chaotic orbit with that of the island in some time interval. This definition allows one to study stickiness systematically on all time scales, including short or nonasymptotic time regimes, as illustrated in the case of an accelerator-mode island of the standard map. A physically significant identification of the "sticky layer" and its "sublayers" in this case is made and discussed.