| 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
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