Global dynamics and stability limits for planetary systems around HD 12661, HD 38529, HD 37124, and HD 160691

In order to distinguish between regular and chaotic planetary orbits, we apply a new technique, called the mean exponential growth factor of nearby orbits (MEGNO), in a wide neighborhood of orbital parameters determined using standard two-body Keplerian fits for the HD 12661, HD 38529, HD 37124, and HD 160691 planetary systems. We show that the currently announced orbital parameters place these systems in very different situations from the point of view of dynamical stability. While HD 38529 and HD 37124 are located within large stability zones in the phase space around their determined orbits, the preliminary orbits in HD 160691 are highly unstable. The orbital parameters of the HD 12661 planets are located in a border region between stable and unstable dynamical regimes, so while its currently determined orbital parameters produce stable regular orbits, a minor change within the margin of error of just one parameter may result in a chaotic dynamical system.