Alica Miller (UIUC)

Characterizations of regular almost periodicity in compact minimal abelian flows (joint work with J. Rosenblatt)

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 of regular almost periodicity (of both, flow and a point in a flow) for the case when the acting group is $\mathbb{R}$. We extend Egawa's results to the case of an arbitrary abelian 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.