On recurrence in zero dimensional flows

J. Auslander*, E. Glasner, B. Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

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, 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 -flow where all points are positively recurrent, but there are points which are not negatively recurrent.

Original languageEnglish
Pages (from-to)107-114
Number of pages8
JournalForum Mathematicum
Volume19
Issue number1
DOIs
StatePublished - 29 Jan 2007

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