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Strongly Recurrent Transformation Groups
Version 1
: Received: 17 December 2021 / Approved: 20 December 2021 / Online: 20 December 2021 (10:28:50 CET)
A peer-reviewed article of this Preprint also exists.
Amini, M.; Swid, J. Strongly Recurrent Transformation Groups. RAIRO - Theoretical Informatics and Applications 2023, 57, 2, doi:10.1051/ita/2023001. Amini, M.; Swid, J. Strongly Recurrent Transformation Groups. RAIRO - Theoretical Informatics and Applications 2023, 57, 2, doi:10.1051/ita/2023001.
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
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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