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Due to the high stellar densities in young clusters, planetary systems formedin these environments are likely to have experienced perturbations fromencounters with other stars. We carry out direct $N$-body simulations ofmulti-planet systems in star clusters to study the combined effects of stellarencounters and internal planetary dynamics. These planetary systems eventuallybecome part of the Galactic field population the parental cluster dissolves,which is where most presently-known exoplanets are observed. We show thatperturbations induced by stellar encounters lead to distinct signatures in thefield planetary systems, most prominently, the excited orbital inclinations andeccentricities. Planetary systems that form within the cluster's half-massradius are more prone to such perturbations. The orbital elements are moststrongly excited in the outermost orbit, but the effect propagates to theentire planetary system through secular evolution. Planet ejections may occurlong after a stellar encounter. The surviving planets in these reduced systemstend to have, on average, higher inclinations and larger eccentricitiescompared to systems that were perturbed less strongly. As soon as the parentalstar cluster dissolves, external perturbations stop affecting the escapedplanetary systems, and further evolution proceeds on a relaxation time scale.The outer regions of these ejected planetary systems tend to relax so slowlythat their state carries the memory of their last strong encounter in the starcluster. Regardless of the stellar density, we observe a robust anticorrelationbetween multiplicity and mean inclination/eccentricity. We speculate that the"Kepler dichotomy" observed in field planetary systems is a natural consequenceof their early evolution in the parental cluster.

The signatures of the parental cluster on field planetary systems