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In this work we numerically explore the Newton-Raphson basins of convergence,related to the equilibrium points, in the Sitnikov three-body problem withnon-spherical primaries. The evolution of the position of the roots isdetermined, as a function of the value of the oblateness coefficient. Theattracting regions, on several types of two dimensional planes, are revealed byusing the classical Newton-Raphson iterative method. We perform a systematicand thorough investigation in an attempt to understand how the oblatenesscoefficient affects the geometry as well as the overall properties of theconvergence regions. The basins of convergence are also related with therequired number of iterations and also with the corresponding probabilitydistributions.

Investigating the basins of convergence in the circular Sitnikov three-body problem with non-spherical primaries