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On recurrence in zero dimensional flows
-
J Auslander
,
E Glasner
Published/Copyright:
February 21, 2007
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 ℤ-flow where all points are positively recurrent, but there are points which are not negatively recurrent.
Received: 2005-04-27
Revised: 2005-08-18
Published Online: 2007-02-21
Published in Print: 2007-01-29
© Walter de Gruyter
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Articles in the same Issue
- Solving Abstract Cauchy Problems with closable operators in reflexive spaces via resolvent-free approximation
- Chain transitive sets for flows on flag bundles
- A Burgess-like subconvex bound for twisted L-functions
- On recurrence in zero dimensional flows
- Solutions of nonlinear elliptic equations in unbounded Lipschitz domains
- π∗(L2T(1)/(v1)) and its applications in computing π∗(L2T(1)) at the prime two
- A proof of the Livingston conjecture
- Expectations of hook products on large partitions and the chi-square distribution
