Submitted:
17 December 2021
Posted:
20 December 2021
You are already at the latest version
Abstract
We define the notions of strong and strict recurrency for actions of countable ordered groups on $\sigma$-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.
Keywords:
ordered groups
; $\sigma$-finite spaces
; strongly recurrent actions
; strictly recurrent actions
; weakly wandering sets
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
