  We carry out N-body simulations to examine the effects of dynamical
interactions on planetary systems in young open star clusters. We explore how
the planetary populations in these star clusters evolve, and how this evolution
depends on the initial amount of substructure, the virial ratio, the cluster
mass and density, and the initial semi-major axis of the planetary systems. The
fraction of planetary systems that remains intact as a cluster member, fbps, is
generally well-described by the functional form fbps=f0(1+[a/a0]^c)^-1, where
(1-f0) is the fraction of stars that escapes from the cluster, a0 the critical
semi-major axis for survival, and c a measure for the width of the transition
region. The effect of the initial amount of substructure over time can be
quantified as fbps=A(t)+B(D), where A(t) decreases nearly linearly with time,
and B(D) decreases when the clusters are initially more substructured. Provided
that the orbital separation of planetary systems is smaller than the critical
value a0, those in clusters with a higher initial stellar density (but
identical mass) have a larger probability of escaping the cluster intact. These
results help us to obtain a better understanding of the difference between the
observed fractions of exoplanets-hosting stars in star clusters and in the
Galactic field. It also allows us to make predictions about the free-floating
planet population over time in different stellar environments.
