  The Copenhagen case of the circular restricted three-body problem with oblate
primary bodies is numerically investigated by exploring the Newton-Raphson
basins of convergence, related to the out-of-plane equilibrium points. The
evolution of the position of the libration points 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 multivariate
Newton-Raphson iterative method. We perform a systematic and thorough
investigation in an attempt to understand how the oblateness coefficient
affects the geometry of the basins of convergence. The convergence regions are
also related with the required number of iterations and also with the
corresponding probability distributions. The degree of the fractality is also
determined by calculating the fractal dimension and the basin entropy of the
convergence planes.
