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.
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