## Product recurrence and distal points

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- by J. Auslander and H. Furstenberg
- Trans. Amer. Math. Soc.
**343**(1994), 221-232 - DOI: https://doi.org/10.1090/S0002-9947-1994-1170562-X
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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.

## References

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## Bibliographic Information

- © Copyright 1994 American Mathematical Society
- 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