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This paper studies the distribution of characteristic multipliers, thestructure of submanifolds, the phase diagram, bifurcations and chaotic motionsin the potential field of rotating highly irregular-shaped celestial bodies(hereafter called irregular bodies). The topological structure of thesubmanifolds for the orbits in the potential field of an irregular body isshown to be classified into 34 different cases, including 6 ordinary cases, 3collisional cases, 3 degenerate real saddle cases, 7 periodic cases, 7period-doubling cases, 1 periodic and collisional case, 1 periodic anddegenerate real saddle case, 1 period-doubling and collisional case, 1period-doubling and degenerate real saddle case, and 4 periodic andperiod-doubling cases. The different distribution of the characteristicmultipliers has been shown to fix the structure of the submanifolds, the typeof orbits, the dynamical behaviour and the phase diagram of the motion.Classifications and properties for each case are presented. Moreover, tangentbifurcations, period-doubling bifurcations, Neimark-Sacker bifurcations and thereal saddle bifurcations of periodic orbits in the potential field of anirregular body are discovered. Submanifolds appear to be Mobius strips andKlein bottles when the period-doubling bifurcation occurs.

Topological Classifications and Bifurcations of Periodic Orbits in the Potential Field of Highly Irregular-shaped Celestial Bodies