Chaos and the Effects of Planetary Migration on the Orbit of S/2000 S5   Kiviuq
  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. 
V. Carruba, D. Nesvorny', J. A. Burns, M. 'Cuk, and K. Tsiganis