A perturbation method for problems with two critical arguments

We develop a semi-numerical perturbation method for problems with two critical arguments. We apply it to a truncated model of the restricted, elliptic three body problem in case of a resonance 2/1 We identify regions of the phase space where chaotic motion is expected because of the presence of homoclinic orbits. One of these regions, the largest one, sits at the entrance to the resonance zone and is associated with a 2/1 resonance between the two critical arguments. The results are compared with numerical results due to Murray (1986)