  We study the dynamics of the 3-D three-body problem of a small body moving
under the attractions of a star and a giant planet which orbits the star on a
much wider and elliptic orbit. In particular, we focus on the influence of an
eccentric orbit of the outer perturber on the dynamics of a small highly
inclined inner body. Our analytical study of the secular perturbations relies
on the classical octupole hamiltonian expansion (third-order theory in the
ratio of the semi-major axes), as third-order terms are needed to consider the
secular variations of the outer perturber and potential secular resonances
between the arguments of the pericenter and/or longitudes of the node of both
bodies. Short-period averaging and node reduction (Laplace plane) reduce the
problem to two degrees of freedom. The four-dimensional dynamics is analyzed
through representative planes which identify the main equilibria of the
problem. As in the circular problem (i.e. perturber on a circular orbit), the
"Kozai-bifurcated" equilibria play a major role in the dynamics of an inner
body on quasi-circular orbit: its eccentricity variations are very limited for
mutual inclination between the orbital planes smaller than ~40^{\deg}, while
they become large and chaotic for higher mutual inclination. Particular
attention is also given to a region around 35^{\deg} of mutual inclination,
detected numerically by Funk et al. (2011) and consisting of long-time stable
and particularly low eccentric orbits of the small body. Using a 12th-order
Hamiltonian expansion in eccentricities and inclinations, in particular its
action-angle formulation obtained by Lie transforms in Libert & Henrard (2008),
we show that this region presents an equality of two fundamental frequencies
and can be regarded as a secular resonance. Our results also apply to binary
star systems where a planet is revolving around one of the two stars.
