This prizewinning PhD thesis presents a general discussion of the orbital motion close to solar
system small bodies (SSSBs) which induce non-central asymmetric gravitational fields in their
neighborhoods. It introduces the methods of qualitative theory in nonlinear dynamics to the
study of local global behaviors around SSSBs. Detailed mechanical models are employed
throughout this dissertation and specific numeric techniques are developed to compensate for
the difficulties of directly analyzing. Applying this method several target systems like
asteroid 216 Kleopatra are explored in great detail and the results prove to be both
revealing and pervasive for a large group of SSSBs.
