  It has recently been shown that stellar clustering plays an important role in
shaping the properties of planetary systems. We investigate how the
multiplicity distributions and orbital periods of planetary systems depend on
the 6D phase space density of stars surrounding planet host systems. We find
that stars in high stellar phase space density environments (overdensities)
have a factor 1.6 - 2.0 excess in the number of single planet systems compared
to stars in low stellar phase space density environments (the field). The
multiplicity distribution of planets around field stars is much flatter (i.e.
there is a greater fraction of multi-planet systems) than in overdensities.
This result is primarily driven by the combined facts that: (i) `hot Jupiters'
(HJs) are almost exclusively found in overdensities; (ii) HJs are predominantly
observed to be single-planet systems. Nevertheless, we find that the difference
in multiplicity is even more pronounced when only considering planets in the
Kepler sample, which contains few HJs. This suggests that the Kepler dichotomy
-- an apparent excess of systems with a single transiting planet -- plausibly
arises from environmental perturbations. In overdensities, the orbital periods
of single-planet systems are smaller than orbital periods of multiple-planet
systems. As this difference is more pronounced in overdensities, the mechanism
responsible for this effect may be enhanced by stellar clustering. Taken
together, the pronounced dependence of planetary multiplicity and orbital
period distributions on stellar clustering provides a potentially powerful tool
to diagnose the impact of environment on the formation and evolution of
planetary systems.
