Directional Recurrence for Infinite Measure Preserving Z^d Actions
Dynamical Systems
2014-08-13 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1306.4357,
title = {Directional Recurrence for Infinite Measure Preserving Z^d Actions},
author = {Aimee S. A. Johnson and Ayse A. Sahin},
journal= {arXiv preprint arXiv:1306.4357},
year = {2014}
}
Comments
Corrections to proof of Proposition 3.3 and other minor edits to assist with readibility. Version to appear in ETDS