  We analyze the structure and stickiness in the chaotic components of generic
Hamiltonian systems with divided phase space. Following the method proposed
recently in Lozej and Robnik [Phys. Rev. E 98, 022220 (2018)], the sticky
regions are identified using the statistics of recurrence times of a single
chaotic orbit into cells dividing the phase space into a grid. We perform
extensive numerical studies of three example systems: the Chirikov standard
map, the family of Robnik billiards, and the family of lemon billiards. The
filling 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 the
description of transport in the phase spaces of ergodic systems. The model is
based on the assumption of completely uncorrelated cell visits because of the
strongly chaotic dynamics of the orbit and the distribution of recurrence times
is exponential. In generic systems the stickiness induces correlations in the
cell visits. The distribution of recurrence times exhibits a separation of
timescales because of the dynamical trapping. We model the recurrence time
distributions to cells inside sticky areas as a mixture of exponential
distributions with different decay times. We introduce the variable S, which is
the ratio between the standard deviation and the mean of the recurrence times
as a measure of stickiness. We use S to globally assess the distributions of
recurrence times. We find that in the bulk of the chaotic sea S=1, while S>1 in
areas of stickiness. We present the results in the form of animated grayscale
plots of the variable S in the largest chaotic component for the three example
systems, included as supplemental material to this paper.
