  Aegaeon, Methone, Anthe, and Pallene are four Saturnian small moons,
discovered by the Cassini spacecraft. Although their orbital characterization
has been carried on by a number of authors, their long-term evolution has not
been studied in detail so far. In this work, we numerically explore the
long-term evolution, up to $10^5$ yr, of the small moons in a system formed by
an oblate Saturn and the five largest moons close to the region: Janus,
Epimetheus, Mimas, Enceladus, and Tethys. By using frequency analysis we
determined the stability of the small moons and characterize, through diffusion
maps, the dynamical behavior of a wide region of geometric phase space, $a$ vs
$e$, surrounding them. Those maps could shed light on the possible initial
number of small bodies close to Mimas, and help to better understand the
dynamical origin of the small satellites. We found that the four small moons
are long-term stable and no mark of chaos is found for them. Aegaeon, Methone,
and Anthe could remain unaltered for at least $\sim0.5$Myr, given the current
configuration of the system. They remain well-trapped in the corotation
eccentricity resonances with Mimas in which they currently librate. However,
perturbations from nearby resonances, such as Lindblad eccentricity resonances
with Mimas, seem responsible for largest variations observed for Methone and
Anthe. Pallene remains in a non-resonant orbit and it is the more stable, at
least for 64 Myr. Nonetheless, it is affected by a quasi-resonance with Mimas,
which induces long-term orbital oscillations of its eccentricity and
inclination.

Earth and Planetary Astrophysics