Product recurrence and distal points

J. AuslÄnder, H. Furstenberg

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish
Pages (from-to)221-232
Number of pages12
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - May 1994
Externally publishedYes


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