Product recurrence and distal points

Authors:
J. Auslander and H. Furstenberg

Journal:
Trans. Amer. Math. Soc. **343** (1994), 221-232

MSC:
Primary 54H20

MathSciNet review:
1170562

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Abstract: Recurrence is studied in the context of actions of compact semigroups on compact spaces. (An important case is the action of the Stone-Čech 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 *F*-recurrent if for some , 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.

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DOI:
https://doi.org/10.1090/S0002-9947-1994-1170562-X

Article copyright:
© Copyright 1994
American Mathematical Society