  The Kozai-Lidov mechanism can be applied to a vast variety of astrophysical
systems involving hierarchical three-body systems. Here, we study the
Kozai-Lidov mechanism systematically in the test particle limit at the octupole
level of approximation. We investigate the chaotic and quasiperiodic orbital
evolution by studying surfaces of section and the Lyapunov exponents. We find
that the resonances introduced by the octupole level of approximation cause
orbits to flip from prograde to retrograde and back as well as cause
significant eccentricity excitation, and the chaotic behaviors occur when the
mutual inclination between the inner and the outer binary is high. We
characterize the parameter space that allows large amplitude oscillations in
eccentricity and inclination.
