  In paper I in this series, we found exact expressions for the equatorial
homoclinic orbits: the separatrix between bound and plunging, whirling and not
whirling. As a companion to that physical space study, in this paper we paint a
phase space portrait of the homoclinic orbits that includes exact expressions
for the actions and fundamental frequencies. Additionally, we develop a reduced
Hamiltonian description of Kerr motion that allows us to track groups of
trajectories with a single global clock. This facilitates a variational
analysis, whose stability exponents and eigenvectors could potentially be
useful for future studies of families of black hole orbits and their associated
gravitational waveforms.
