Or in other words, are there differences in average Lyapunov timescale between orbits interior to Jupiter and orbits exterior to Jupiter? I'm trying to answer a question at http://www.quora.com/Why-does-Pluto-have-so-many-satellites/answer/Alex-K-Chen but I'm not totally sure if the last part of my answer is right. I'll quote the last part of it:
If the 2nd theory is true, then it's harder to answer this. One thing for sure though: Jupiter is much farther away, so its tug on the system is a much smaller factor than it is for the inner planets (where it can be a major source of instability over the solar system's lifetime)
In fact - I suspect that another factor is that from Pluto's perspective, Jupiter is practically in the center of the solar system anyways, so you're unlikely to see periods of time where Jupiter is in such a position where its constant gravitational tugs (over several Jupiter orbits) can accumulate and tug a satellite into an unstable orbit (which is what can happen with planets that orbit the Sun at distances interior to Jupiter ). Anyways I don't fully know the physics on this (yet) so some of my details could be wrong - what I do know is that it could happen to both asteroid belt objects and to Mercury's orbit - http://en.wikipedia.org/wiki/Stability_of_the_Solar_System#Mercury.E2.80.93Jupiter_1:1_resonance - perhaps because there are positions where Jupiter's pull on interior bodies is in a direction opposite to that of the Sun's pull (we never hear about the Sun creating any orbital instabilities). And Mercury is much closer to Jupiter than Pluto is.
Of course, Pluto is vulnerable to Neptune's influence, but Pluto and Neptune have a 3:2 orbital resonance so it's relatively safe from collisions with Neptune (although the resonance may not be constant over the solar system's lifetime)
Anyways, we might finally know more once New Horizons reaches Pluto in a few years
 http://www.alpheratz.net/murison/papers/Lyapunov/LFM.pdf says that there is something special about asteroids with orbits interior to Jupiter - I'll try to find more information on this.