  Among the many new irregular satellites that have been discovered in the last
five years, at least six are in the so-called Kozai resonance. Due to solar
perturbations, the argument of pericenter of a satellite usually precesses from
0 to 360 degrees. However, at inclinations higher than 39.3 degrees and lower
than 140.7 degrees a new kind of behavior occurs for which the argument of
pericenter oscillates around +/-90 degrees. In this work we will concentrate on
the orbital history of the saturnian satellite S/2000 S5 Kiviuq, one of the
satellites currently known to be in such resonance Kiviuq's orbit is very close
to the separatrix of the Kozai resonance. Due to perturbations from the other
jovian planets, it is expected that orbits near the Kozai separatrix may show
significant chaotic behavior. This is important because chaotic diffusion may
transfer orbits from libration to circulation, and vice versa. To identify
chaotic orbits we used two well-known methods: the Frequency Analysis Method
(Laskar 1990) and Maximum Lyapunov Exponents (Benettin et al. 1980). Our
results show that the Kozai resonance is crossed by a web of secondary
resonances, whose arguments involve combinations of the argument of pericenter,
the argument of the Great Inequality, longitude of the node, and other terms
related to the secular frequencies g5, g6, and s6. Many test orbits whose
precession period is close to the period of the Great Inequality (883 yrs), or
some of its harmonics, are trapped by these secondary resonances, and show
significant chaotic behavior. Planetary migration, by moving the locations of
these secondary resonances, may have depleted an original population of Kozai
resonators.
