  We describe the families of periodic orbits in the 2-dimensional 1/2
retrograde resonance at mass ratio 0.001, analyzing their stability and
bifurcations into 3-dimensional periodic orbits. We explain the role played by
periodic orbits in adiabatic resonance capture, in particular how the proximity
between a stable family and an unstable family with a nearly critical segment,
associated with Kozai separatrices, determines the transition between distinct
resonant modes observed in numerical simulations. Combining the identification
of stable, critical and unstable periodic orbits with analytical modeling,
resonance capture simulations and computation of stability maps helps to unveil
the complex 3-dimensional structure of resonances.
