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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Product recurrence and distal points


Authors: J. Auslander and H. Furstenberg
Journal: Trans. Amer. Math. Soc. 343 (1994), 221-232
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9947-1994-1170562-X
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 $ px = x$ for some $ p \in 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.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1170562-X
Article copyright: © Copyright 1994 American Mathematical Society