On recurrence in zero dimensional flows

被引：30

作者：

Auslander, J. ^{[1
]}

Glasner, E.

Weiss, B.

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Tel Aviv Univ, Dept Math, IL-69978 Tel Aviv, Israel

[3] Hebrew Univ Jerusalem, Math Inst, IL-91905 Jerusalem, Israel

来源：

FORUM MATHEMATICUM | 2007年 / 19卷 / 01期

关键词：

D O I：

10.1515/FORUM.2007.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an action of a finitely generated group G on a compact space X we define recurrence at a point and then show that, when X is zero dimensional, the conditions (i) pointwise recurrence, (ii) X is a union of minimal sets and (iii) the orbit closure relation is closed in X x X, are equivalent. As a corollary we get that for such flows distality is the same as equicontinuity. In the last part of the paper we describe an example of a Z-flow where all points are positively recurrent, but there are points which are not negatively recurrent.

引用

页码：107 / 114

页数：8