  In this work we numerically explore the Newton-Raphson basins of convergence,
related to the equilibrium points, in the Sitnikov three-body problem with
non-spherical primaries. The evolution of the position of the roots is
determined, as a function of the value of the oblateness coefficient. The
attracting regions, on several types of two dimensional planes, are revealed by
using the classical Newton-Raphson iterative method. We perform a systematic
and thorough investigation in an attempt to understand how the oblateness
coefficient affects the geometry as well as the overall properties of the
convergence regions. The basins of convergence are also related with the
required number of iterations and also with the corresponding probability
distributions.
