  The Newton-Raphson basins of attraction, associated with the libration points
(attractors), are revealed in the generalized Hill problem. The parametric
variation of the position and the linear stability of the equilibrium points is
determined, when the value of the perturbation parameter $\epsilon$ varies. The
multivariate Newton-Raphson iterative scheme is used to determine the
attracting domains on several types of two-dimensional planes. A systematic and
thorough numerical investigation is performed in order to demonstrate the
influence of the perturbation parameter on the geometry as well as of the basin
entropy of the basins of convergence. The correlations between the basins of
attraction and the corresponding required number of iterations are also
illustrated and discussed. Our numerical analysis strongly indicates that the
evolution of the attracting regions in this dynamical system is an extremely
complicated yet very interesting issue.
