  We present a comparative study of several dynamical systems of increasing
complexity, namely, the logistic map with additive noise, one, two and many
globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the
classical inertial infinitely-ranged ferromagnetically coupled XY spin model).
We emphasize the appearance, in all of these systems, of metastable states and
their ultimate crossover to the equilibrium state. We comment on the underlying
mechanisms responsible for these phenomena (weak chaos) and compare common
characteristics. We point out that this ubiquitous behavior appears to be
associated to the features of the nonextensive generalization of the
Boltzmann-Gibbs statistical mechanics.
