We consider the Gyldén problem—a perturbation of the Kepler problem via an explicit function of time. For certain general classes of planar periodic perturbations, after proving a Poincaré–Melnikov-type criterion, we find a manifold of orbits in which the dynamics is given by the shift automorphism on the set of bi-infinite sequences with infinitely many symbols. We achieve the main result by computing the Melnikov integral explicitly.
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Diacu et al. (1998) studied this question.
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