We explore the region of influence of a galaxy cluster using numerical
simulations of cold dark matter halos. Many of the observed galaxies in a
cluster are expected to be infalling for the first time. Half of the halos at
distances of one to two virial radii today have previously orbited through the
cluster, most of them have even passed through the dense inner regions of the
cluster. Some halos at distances of up to three times the virial radius have
also passed through the cluster core. We do not find a significant correlation
of ``infall age'' versus present day position for substructures and the scatter
at a given position is very large. This relation may be much more significant
if we could resolve the physically overmerged galaxies in the central region.Comment: To appear in the proceedings of IAU Colloquium 195: "Outskirts of
galaxy clusters: intense life in the suburbs", Torino, Italy, March 12-16,
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