Dynamical study while searching equilibrium solutions in N-body problem

The theory of complex dynamics is usually applied to compare the global convergence properties of different iterative methods, by obtaining the attraction basins for simple polynomial equations in the complex domain. However, in this work, we use it in quite another context: the study of a nontrivial nonlinear system that describes the motion of interacting bodies in celestial mechanics, namely, Newtonian planar circular restricted four‐body problem and its relative equilibrium solutions. These have been investigated from a dynamical point of view. New properties of the solutions of this system have been obtained. Practical guidelines for efficient search of relative equilibrium solutions of $N$ ‐body problem have been given.