TY - JOUR

T1 - Product recurrence and distal points

AU - AuslÄnder, J.

AU - Furstenberg, H.

PY - 1994/5

Y1 - 1994/5

N2 - Recurrence is studied in the context of actions of compact semigroups on compact spaces. (An important case is the action of the Stone-Cech compactification of an acting group.) If the semigroup E acts on the space X and F is a closed subsemigroup of E, then x in X is said to be Frecurrent if px = x for some p ∈ F, and product F-recurrent 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 main result is that, under certain conditions, a point is product F-recurrent if and only if it is a distal point.

AB - Recurrence is studied in the context of actions of compact semigroups on compact spaces. (An important case is the action of the Stone-Cech compactification of an acting group.) If the semigroup E acts on the space X and F is a closed subsemigroup of E, then x in X is said to be Frecurrent if px = x for some p ∈ F, and product F-recurrent 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 main result is that, under certain conditions, a point is product F-recurrent if and only if it is a distal point.

UR - http://www.scopus.com/inward/record.url?scp=84966241665&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1994-1170562-X

DO - 10.1090/S0002-9947-1994-1170562-X

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AN - SCOPUS:84966241665

SN - 0002-9947

VL - 343

SP - 221

EP - 232

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 1

ER -