Chaos in the Gylden problem

We consider the Gylden problem-a perturbation of the Kepler problem via an explicit function of time. For certain general classes of planar periodic p erturbations, after proving a Poincare'-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 achie ve the main result by computing the Melnikov integral explicitly. (C) 1998 American Institute of Physics. [S0022-2488(98)01912-4].