  We aim to locate the stability region for Uranus Trojans (UT hereafter) and
find out the dynamical mechanisms responsible for the structures in the phase
space. Using the spectral number as the stability indicator, we construct the
dynamical maps on the (a0, i0) plane. The proper frequencies of UTs are
determined precisely so that we can depict the resonance web via a
semi-analytical method. Two main stability regions are found, one each for the
low-inclination (0-14deg) and high-inclination regime (32-59deg). There is also
an instability strip in each of them, at 9deg and 51deg respectively. All
stability regions are in the tadpole regime and no stable horseshoe orbits
exist for UTs. The lack of moderate-inclined UTs is caused by the nu5 and nu7
secular resonances. The fine structures in the dynamical maps are shaped by
high-degree secular resonances and secondary resonances. During the planetary
migration, about 36.3% and 0.4% of the pre-formed orbits survive the fast and
slow migrations (with migrating time scales of 1 and 10Myr) respectively, most
of which are in high inclination. Since the low-inclined UTs are more likely to
survive the age of the solar system, they make up 77% of all such long-life
orbits by the end of the migration, making a total fraction up to 4.06E-3 and
9.07E-5 of the original population for the fast and slow migrations,
respectively. About 3.81% UTs are able to survive the age of the solar system,
among which 95.5% are on low-inclined orbits with i0<7.5deg. However, the
depletion of the planetary migration seems to prevent a large fraction of such
orbits, especially for the slow migration model.
