PRODUCT RECURRENCE AND DISTAL POINTS

Recurrence is studied in the context of actions of compact semigroups on compact spaces. (An important caw is the action of the Stone-Cech c ompactification of an acting group.) If the semigroup E acts on the sp ace X and F is a closed subsemigroup of E, then x in x is said to be F -recurrent if px = x for some p is-an-element-of F, and product F-recu rrent if whenever y is an F-recurrent point (in some space Y on which E acts) the point (x, y) in the product system is F-recurrent. The mai n result is that, under certain conditions, a point is product F-recur rent if and only if it is a distal point.