Directional recurrence for infinite measure preserving Zd actions

被引:4
|
作者
Johnson, Aimee S. A. [1 ]
Sahin, Ayse A. [2 ]
机构
[1] Swarthmore Coll, Dept Math & Stat, Swarthmore, PA 19081 USA
[2] De Paul Univ, Dept Math Sci, Chicago, IL 60626 USA
关键词
RANK-ONE;
D O I
10.1017/etds.2014.17
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We define directional recurrence for infinite measure preserving Z(d) actions both intrinsically and via the unit suspension flow and prove that the two definitions are equivalent. We study the structure of the set of recurrent directions and show it is always a G(delta) set. We construct an example of a recurrent action with no recurrent directions, answering a question posed in a 2007 paper of Daniel J. Rudolph. We also show by example that it is possible for a recurrent action to not be recurrent in an irrational direction even if all its sub-actions are recurrent.
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页码:2138 / 2150
页数:13
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