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In this study, equilibrium points and periodic orbits in the potential fieldof asteroids are investigated. We present the linearized equations of motionrelative to the equilibrium points and characteristic equations. We find thatthe distribution of characteristic multipliers of periodic orbits around theequilibrium point and the distribution of eigenvalues of the equilibrium pointcorrespond to each other. The distribution of eigenvalues of the equilibriumpoint confirms the topology and the stability of periodic orbits around theequilibrium point.

Equilibrium Points and Periodic Orbits in the Vicinity of Asteroids with an Application to 216 Kleopatra