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

A study of the 1/2 retrograde resonance: Periodic orbits and resonant capture