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 quasi-periodic orbital evolution by studying the 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 chaotic behavior occurs 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.
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