Chaos around the superposition of a monopole and a thick disk

We extend recent investigations on the integrability of oblique orbits of t est particles under the gravitational field corresponding to the superposit ion of an infinitesimally thin disk and a monopole to the more realistic ca se, for astrophysical purposes, of a thick disk. Exhaustive numerical analy ses were performed and the robustness of the recent results is confirmed. W e also found that, for smooth distributions of matter, the disk thickness c an attenuate the chaotic behavior of the bounded oblique orbits. Perturbati ons leading to the breakdown of the reflection symmetry about the equatoria l plane, nevertheless, may enhance significantly the chaotic behavior, in a greement with recent studies on oblate models. (C) 2000 Elsevier Science B. V. All rights reserved.