On the survival of resonant and non-resonant planetary systems in star
  clusters
  Despite the discovery of thousands of exoplanets in recent years, the number
of known exoplanets in star clusters remains tiny. This may be a consequence of
close stellar encounters perturbing the dynamical evolution of planetary
systems in these clusters. Here, we present the results from direct $N$-body
simulations of multiplanetary systems embedded in star clusters containing $N =
8k, 16k, 32k$, and $64k$ stars. The planetary systems, which consist of the
four Solar system giant planets Jupiter, Saturn, Uranus, and Neptune, are
initialized in different orbital configurations, to study the effect of the
system architecture on the dynamical evolution of the entire planetary system,
and on the escape rate of the individual planets. We find that the current
orbital parameters of the Solar system giants (with initially circular orbits,
as well as with present-day eccentricities) and a slightly more compact
configuration, have a high resilience against stellar perturbations. A
configuration with initial mean-motion resonances of 3:2, 3:2, and 5:4 between
the planets, which is inspired by the Nice model, and for which the two
outermost planets are usually ejected within the first $10^5$ yr, is in many
cases stabilized due to the removal of the resonances by external stellar
perturbation and by the rapid ejection of at least one planet. Assigning all
planets the same mass of 1 Jovian mass almost equalizes the survival fractions.
Our simulations reproduce the broad diversity amongst observed exoplanet
systems. We find not only many very wide and/or eccentric orbits, but also a
significant number of (stable) retrograde orbits.
