We propose recurrence plots (RPs) to characterize the stickiness of a typical area-preserving map with coexisting chaotic and regular orbits. The difference of the recurrence properties between quasiperiodic and chaotic orbits is revisited, which helps to understand the complex patterns of the corresponding RPs. Moreover, several measures from the recurrence quantification analysis are used to quantify these patterns. Among these measures, the recurrence rate, quantifying the percentage of black points in the plot, is applied to characterize the stickiness of a typical chaotic orbit. The advantage of the recurrence based method in comparison to other standard techniques is that it is possible to distinguish between quasiperiodic and chaotic orbits that are temporarily trapped in a sticky domain, from very short trajectories.
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In our computations, 500 initial values are chosen randomly. From these trajectories several typical orbits are represented to be computer memory efficient. If we did not proceed so, a figure like Fig. 1(a) would require approximately of hard-disk space. There are no trajectories in the white regions of Fig. 1 for the initial values we choose, which are excluded from the color bar.
