  A three-dimensional dynamical model for a galaxy hosting a BL Lacertae object
is constructed. The model consists of a logarithmic potential representing an
elliptical host galaxy with a bulge of radius $c_b$ and a dense massive
nucleus. Using numerical experiments, we try to distinguish between regular and
chaotic motion in both 2D and 3D system. In particular, we investigate how the
basic parameters of our model, such as the mass of the nucleus, the internal
perturbation and the flattening parameters influence the amount and the degree
of chaos. Interesting correlations are presented for both 2D and 3D dynamical
models. Our numerical results are explained and supported using elementary
theoretical arguments and analytical calculations. Of particular interest, is
the local integral of motion which have been found to exist in the vicinity of
stable periodic points. The obtained numerical outcomes of the present
research, are linked and also compared with several data derived from
observations.
