  In this work we present the results of a suite of dynamical simulations
following the orbital evolution of 8,022 hypothetical Centaur objects. These
Centaurs begin our integrations on orbits in the vicinity of the 2:1 mean
motion resonance with Neptune, and we follow their dynamical evolution for a
period of 3 Myr under the gravitational influence of a motionless Sun and the
four Jovian planets. The great majority of the test particles studied rapidly
escaped from the vicinity of the 2:1 mean motion resonance of Neptune and
diffused throughout the Solar System. The average libration time of Centaurs in
the vicinity of 2:1 mean motion resonance of Neptune was found to be just 27
kyr. Although two particles did remain near the resonance for more than 1 Myr.
Upon leaving the vicinity of the 2:1 resonance, the majority of test particles
evolved by a process of random walk in semi-major axis, due to repeated close
encounters with the giant planets.
