| Issue |
RAIRO-Theor. Inf. Appl.
Volume 57, 2023
|
|
|---|---|---|
| Article Number | 2 | |
| Number of page(s) | 8 | |
| DOI | https://doi.org/10.1051/ita/2023001 | |
| Published online | 27 February 2023 | |
Strongly Recurrent Transformation Groups
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran
* Corresponding author: mamini@modares.ac.ir
Received:
23
May
2022
Accepted:
26
January
2023
We define the notions of strong and strict recurrency for actions of countable ordered groups on σ-finite non atomic measure spaces with quasi-invariant measures. We show that strong recurrency is equivalent to non existence of weakly wandering sets of positive measure. We also show that for certain p.m.p ergodic actions the system is not strictly recurrent, which shows that strong and strict recurrency are not equivalent.
Mathematics Subject Classification: 22F10 / 37A05
Key words: Ordered groups / σ-finite spaces / strongly recurrent actions / strictly recurrent actions / weakly wandering sets
© The authors. Published by EDP Sciences, 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.