  We numerically investigate the long-term dynamics of the Saturn's small
satellites Methone (S/2004 S1), Anthe (S/2007 S4) and Pallene (S/2004 S2). In
our numerical integrations, these satellites are disturbed by non-spherical
shape of Saturn and the six nearest regular satellites. The stability of the
small bodies is studied here by analyzing long-term evolution of their orbital
elements.
  We show that long-term evolution of Pallene is dictated by a quasi secular
resonance involving the ascending nodes ($\Omega$) and longitudes of
pericentric distances ($\varpi$) of Mimas (subscript 1) and Pallene (subscript
2), which critical argument is $\varpi_2-\varpi_1-\Omega_1+\Omega_2$. Long-term
orbital evolution of Methone and Anthe are probably chaotic since: i) their
orbits randomly cross the orbit of Mimas in time scales of thousands years);
ii) numerical simulations involving both small satellites are strongly affected
by small changes in the initial conditions.

Earth and Planetary Astrophysics