  We investigate the regular or chaotic nature of orbits of stars moving in the
meridional plane $(R,z)$ of an axially symmetric galactic model with a flat
disk and a central, non spherical and massive nucleus. In particular, we study
the influence of the flattening parameter of the central nucleus on the nature
of orbits, by computing in each case the percentage of chaotic orbits, as well
as the percentages of orbits of the main regular families. In an attempt to
maximize the accuracy of our results upon distinguishing between regular and
chaotic motion, we use both the Fast Lyapunov Indicator (FLI) and the Smaller
ALingment Index (SALI) methods to extensive samples of orbits obtained by
integrating numerically the equations of motion as well as the variational
equations. Moreover, a technique which is based mainly on the field of spectral
dynamics that utilizes the Fourier transform of the time series of each
coordinate is used for identifying the various families of regular orbits and
also to recognize the secondary resonances that bifurcate from them. Varying
the value of the flattening parameter, we study three different cases: (i) the
case where we have a prolate nucleus (ii) the case where the central nucleus is
spherical and (iii) the case where an oblate massive nucleus is present.
Furthermore, we present some additional findings regarding the reliability of
short time (fast) chaos indicators, as well as a new method to define the
threshold between chaos and regularity for both FLI and SALI, by using them
simultaneously. Comparison with early related work is also made.
