## Characterizations of regular almost periodicity in compact minimal abelian flows

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- by Alica Miller and Joseph Rosenblatt PDF
- Trans. Amer. Math. Soc.
**356**(2004), 4909-4929 Request permission

## Abstract:

Regular almost periodicity in compact minimal abelian flows was characterized for the case of discrete acting group by W. Gottschalk and G. Hedlund and for the case of $0$-dimensional phase space by W. Gottschalk a few decades ago. In 1995 J. Egawa gave characterizations for the case when the acting group is $\mathbb {R}$. We extend Egawa’s results to the case of an arbitrary abelian acting group and a not necessarily metrizable phase space. We then show how our statements imply previously known characterizations in each of the three special cases and give various other applications (characterization of regularly almost periodic functions on arbitrary abelian topological groups, classification of uniformly regularly almost periodic compact minimal $\mathbb {Z}$- and $\mathbb {R}$-flows, conditions equivalent with uniform regular almost periodicity, etc.).## References

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## Additional Information

**Alica Miller**- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
- Email: amiller@math.uiuc.edu
**Joseph Rosenblatt**- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
- MR Author ID: 150595
- Email: jrsnbltt@math.uiuc.edu
- Received by editor(s): November 3, 2002
- Received by editor(s) in revised form: June 19, 2003
- Published electronically: February 4, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**356**(2004), 4909-4929 - MSC (2000): Primary 37B05, 43A60; Secondary 43A40, 54H20
- DOI: https://doi.org/10.1090/S0002-9947-04-03538-X
- MathSciNet review: 2084405