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The present work studies the robustness of certain basic homoclinic motionsin an equilateral restricted four body problem. The problem can be viewed as atwo parameter family of conservative autonomous vector fields. The main toolsare numerical continuation techniques for homoclinic and periodic orbits, aswell as formal series methods for computing normal forms and centerstable/unstable manifold parameterizations. After careful numerical study of anumber of special cases we formulate several conjectures about the globalbifurcations of the homoclinic families.

Critical homoclinics in a restricted four body problem: numerical continuation and center manifold computations