  We perform a detailed study of the chaotic component in mixed-type
Hamiltonian systems on the example of a family of billiards [introduced by
Robnik in J. Phys. A: Math. Gen. 16, 3971 (1983)]. The phase space is divided
into a grid of cells and a chaotic orbit is iterated a large number of times.
The structure of the chaotic component is discerned from the cells visited by
the chaotic orbit. The fractal dimension of the border of the chaotic component
for various values of the billiard shape parameter is determined with the
box-counting method. The cell-filling dynamics is compared to a model of
uncorrelated motion, the so-called random model [Robnik et al. J. Phys. A:
Math. Gen. 30, L803 (1997)], and deviations attributed to sticky objects in the
phase space are found. The statistics of the number of orbit visits to the
cells is analyzed and found to be in agreement with the random model in the
long run. The stickiness of the various structures in the phase space is
quantified in terms of the cell recurrence times. The recurrence time
distributions in a few selected cells as well as the mean and standard
deviation of recurrence times for all cells are analyzed. The standard
deviation of cell recurrence time is found to be a good quantifier of
stickiness on a global scale. Three methods for determining the measure of the
chaotic component are compared and the measure is calculated for various values
of the billiard shape parameter. Lastly, the decay of correlations and the
diffusion of momenta is analyzed.
