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The order and chaos of the motion near equilibrium points in the potential ofa rotating highly irregular-shaped celestial body are investigated from pointof view of the dynamical system theory. The positions of the non-degenerateequilibrium points vary continuously when the parameter changes. Thetopological structures in the vicinity of equilibrium points are classifiedinto several different cases. Bifurcations at equilibrium points and thetopological transfers between different cases for equilibrium points are alsodiscussed. The conclusions can be applied to all kinds of rotating celestialbodies, simple-shaped or highly irregular-shaped, including asteroids, comets,planets and satellites of planets to help one to understand the dynamicalbehaviors around them. Applications to asteroids 216 Kleopatra, 2063 Bacchus,and 25143 Itokawa are significant and interesting: eigenvalues affiliated tothe equilibrium points for the asteroid 216 Kleopatra move and always belong tothe same topological cases; while eigenvalues affiliated to two differentequilibrium points for the asteroid 2063 Bacchus and 25143 Itokawa move throughthe resonant cases of equilibrium points, and the collision of eigenvalues inthe complex plane occurs. Poincar\'e sections in the potential of the asteroid216 Kleopatra show the chaos behaviors of the orbits in large scale.

Order and Chaos near Equilibrium Points in the Potential of Rotating Highly Irregular-shaped Celestial Bodies