  We define directional recurrence for infinite measure preserving Z^d actions
both intrinsically and via the unit suspension flow and prove that the two
definitions are equivalent. We study the structure of the set of recurrent
directions and show it is always a G_delta set. We construct an example of a
recurrent action with no recurrent directions, answering a question posed in a
2007 paper of Daniel J. Rudolph. We also show by example that it is possible
for a recurrent action to not be recurrent in an irrational direction even if
all its sub-actions are recurrent.
