  In recent years, statistical characterization of the discrete conservative
dynamical systems (more precisely, paradigmatic examples of area-preserving
maps such as the standard and the web maps) has been analyzed extensively and
shown that, for larger parameter values for which the Lyapunov exponents are
largely positive over the entire phase space, the probability distribution is a
Gaussian, consistent with Boltzmann-Gibbs (BG) statistics. On the other hand,
for smaller parameter values for which the Lyapunov exponents are virtually
zero over the entire phase space, we verify this distribution appears to
approach a $q$-Gaussian (with $q \simeq 1.935$), consistent with
$q$-statistics. Interestingly, if the parameter values are in between these two
extremes, then the probability distributions happen to exhibit a linear
combination of these two behaviours. Here, we numerically show that the Harper
map is also in the same universality class of the maps discussed so far. This
constitutes one more evidence on the robustness of this behavior whenever the
phase space consists of stable orbits. Then, we propose a generalization of the
standard map for which the phase space includes many sticky regions, changing
the previously observed simple linear combination behavior to a more complex
combination.
