Centaurs are small bodies orbiting between Jupiter and Neptune that were scattered inwards from their sources in the trans-Neptunian region, and which will eventually feed the JFC population. A small fraction of Centaurs display comet-like activity, of which the the drivers and triggers are not well understood. The range of heliocentric distances where the active Centaurs have been observed, and their median lifetime in the region, suggest this activity is neither driven by water-ice sublimation, nor entirely by super-volatiles.
Here we present a dynamical study of 55 active Centaurs and high-perihelion JFCs and compare their dynamical behaviors to those of more than 260 known inactive objects in the region. Our results suggest there is a common feature present in the orbital evolution of active bodies — a sudden rapid decrease in semi-major axis occurring less than several hundred years in the past. This 'a-dip' can be seen in the orbital history of only a small fraction of seemingly inactive Centaurs, and in most cases it is not correlated with a substantial change in perihelion distance. The sudden decrease in semi-major axis could act as a trigger for the cometary activity on Centaurs due to the change of thermal environment and the lag between the a-jump and some recently observed active Centaurs could be use to constraint the volatiles and processes driving the cometary activity beyond the orbit of Jupiter. We have identified eight Centaur candidates with no observed prior periods of activity for possible future outbursts based on their recent dips in semi-major axis observed in other active Centaurs and distant JFCs. These objects should be targets of high interest for observational activity monitoring.