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We analyze the structure and stickiness in the chaotic components of genericHamiltonian systems with divided phase space. Following the method proposedrecently in Lozej and Robnik [Phys. Rev. E 98, 022220 (2018)], the stickyregions are identified using the statistics of recurrence times of a singlechaotic orbit into cells dividing the phase space into a grid. We performextensive numerical studies of three example systems: the Chirikov standardmap, the family of Robnik billiards, and the family of lemon billiards. Thefilling of the cells is compared to the random model of chaotic diffusion,introduced in Robnik et al. [J. Phys. A: Math. Gen. 30, L803 (1997)] for thedescription of transport in the phase spaces of ergodic systems. The model isbased on the assumption of completely uncorrelated cell visits because of thestrongly chaotic dynamics of the orbit and the distribution of recurrence timesis exponential. In generic systems the stickiness induces correlations in thecell visits. The distribution of recurrence times exhibits a separation oftimescales because of the dynamical trapping. We model the recurrence timedistributions to cells inside sticky areas as a mixture of exponentialdistributions with different decay times. We introduce the variable S, which isthe ratio between the standard deviation and the mean of the recurrence timesas a measure of stickiness. We use S to globally assess the distributions ofrecurrence times. We find that in the bulk of the chaotic sea S=1, while S>1 inareas of stickiness. We present the results in the form of animated grayscaleplots of the variable S in the largest chaotic component for the three examplesystems, included as supplemental material to this paper.

Stickiness in generic low-dimensional Hamiltonian systems: A recurrence-time statistics approach