  The dynamics of artificial asteroids on the Trojan-like orbits around Neptune
is investigated in this paper. We describe the dependence of the orbital
stability on the initial semimajor axis a and inclination i by constructing a
dynamical map on the (a,i)-plane. Rich details are revealed in the dynamical
map, especially a unstable gap at i=45 deg is determined and the mechanism
triggering chaos in this region is figured out. Our investigation can be used
to guide the observations.
