  We present results of numerical simulations which examine the dynamical
stability of known planetary systems, a star with two or more planets. First we
vary the initial conditions of each system based on observational data. We then
determine regions of phase space which produce stable planetary configurations.
For each system we perform 1000 ~1 million year integrations. We examine
upsilon And, HD83443, GJ876, HD82943, 47UMa, HD168443, and the solar system
(SS). We find that the resonant systems, 2 planets in a first order mean motion
resonance, (HD82943 and GJ876) have very narrow zones of stability. The
interacting systems, not in first order resonance, but able to perturb each
other (upsilon And, 47UMa, and SS) have broad regions of stability. The
separated systems, 2 planets beyond 10:1 resonance, (we only examine HD83443
and HD168443) are fully stable. Furthermore we find that the best fits to the
interacting and resonant systems place them very close to unstable regions. The
boundary in phase space between stability and instability depends strongly on
the eccentricities, and (if applicable) the proximity of the system to perfect
resonance. In addition to million year integrations, we also examined stability
on ~100 million year timescales. For each system we ran ~10 long term
simulations, and find that the Keplerian fits to these systems all contain
configurations which may be regular on this timescale.
