  The significant orbital eccentricities of most giant extrasolar planets may
have their origin in the gravitational dynamics of initially unstable multiple
planet systems. In this work, we explore the dynamics of two close planets on
inclined orbits through both analytical techniques and extensive numerical
scattering experiments. We derive a criterion for two equal mass planets on
circular inclined orbits to achieve Hill stability, and conclude that
significant radial migration and eccentricity pumping of both planets occurs
predominantly by 2:1 and 5:3 mean motion resonant interactions. Using
Laplace-Lagrange secular theory, we obtain analytical secular solutions for the
orbital inclinations and longitudes of ascending nodes, and use those solutions
to distinguish between the secular and resonant dynamics which arise in
numerical simulations. We also illustrate how encounter maps, typically used to
trace the motion of massless particles, may be modified to reproduce the gross
instability seen by the numerical integrations. Such a correlation suggests
promising future use of such maps to model the dynamics of more coplanar
massive planet systems.
