Resumen
We investigate the topological types and bifurcations of periodic orbits in the gravitational field of irregular bodies by the well-known two parameter analysis method. Results show that the topological types of periodic orbits are determined by the locations of these two parameters and that the bifurcation types correspond to their variation paths in the plane. Several new paths corresponding to doubling period bifurcations, tangent bifurcations and Neimark?Sacker bifurcations are discovered. Then, applications in detecting bifurcations of periodic orbits near asteroids 101955 Bennu and 2867 Steins are presented. It is found that tangent bifurcations may occur three times when continuing the vertical orbits near the equilibrium points of 101955 Bennu. The continuation stops as the Jacobi energy reaches a local maximum. However, while continuing the vertical orbits near the equilibrium points of 2867 Steins, the tangent bifurcation and pseudo period-doubling bifurcation occur. The continuation can always go on, and the orbit ultimately becomes nearly circular.