  We present the results of "snapshot" numerical integrations of test particles
representing comet-like and asteroid-like objects in the inner solar system
aimed at investigating the short-term dynamical evolution of objects close to
the dynamical boundary between asteroids and comets as defined by the Tisserand
parameter with respect to Jupiter, T_J (i.e., T_J=3). As expected, we find that
T_J for individual test particles is not always a reliable indicator of initial
orbit types. Furthermore, we find that a few percent of test particles with
comet-like starting elements (i.e., similar to Jupiter-family comets) reach
main-belt-like orbits (at least temporarily) during our 2 Myr integrations,
even without the inclusion of non-gravitational forces, apparently via a
combination of gravitational interactions with the terrestrial planets and
temporary trapping by mean-motion resonances with Jupiter. We estimate that the
fraction of real Jupiter-family comets occasionally reaching main-belt-like
orbits on Myr timescales could be on the order of ~0.1-1%, although the
fraction that remain on such orbits for appreciable lengths of time is
certainly far lower. Thus, the number of JFC-like interlopers in the main-belt
population at any given time is likely to be small, but still non-zero, a
finding with significant implications for efforts to use main-belt comets to
trace the primordial distribution of volatile material in the inner solar
system. The test particles with comet-like starting orbital elements that
transition onto main-belt-like orbits in our integrations appear to be largely
prevented from reaching low eccentricity, low inclination orbits. We therefore
find that low-eccentricity, low-inclination main-belt comets may provide a more
reliable means for tracing the primordial ice content of the main asteroid belt
than the main-belt comet population as a whole.
