@article{031748e62d93459b81e4c19e22df29f8,
title = "W-measurable sensitivity of semigroup actions",
abstract = "This paper studies the notion of W-measurable sensitivity in the context of countable semigroup actions. W-measurable sensitivity is a measurable generalization of sensitive dependence on initial conditions. In 2012, Grigoriev et al. proved a classifica-tion result of conservative ergodic nonsingular dynamical systems which states that all are either W-measurably sensitive or act by isometries with respect to some metric and have refined structure. We generalize this result to a class of semigroup actions. Furthermore, a counterexample is provided showing that W-measurable sensitivity is not preserved under factors. We also consider the restriction of W-measurably sensitive semigroup actions to subsemigroups and show that the restriction remains W-measurably sensitive when the subsemigroup is large enough (e.g. when the subsemigroups are syndetic or thick).",
keywords = "Ergodic, Nonsingular transformation, Sensitive dependence, measure-preserving",
author = "Francisc Bozgan and Anthony Sanchez and Silva, {Cesar E.} and Jack Spielberg and David Stevens and Jane Wang",
note = "Funding Information: Acknowledgements. This research was initiated by the Ergodic Theory group of the 2013 SMALL Undergraduate Research program at Williams College with support provided by the National Science Foundation REU Grant DMS-0850577 and the Science Center of Williams College. Both JW and AS were supported by the National Science Foundation Graduate Research Fellowship under Grants No. 1256082 and No. 1122374, respectively. Funding Information: This research was initiated by the Ergodic Theory group of the 2013 SMALL Undergraduate Research program at Williams College with support provided by the National Science Foundation REU Grant DMS-0850577 and the Science Center of Williams College. Both JW and AS were supported by the National Science Foundation Graduate Research Fellowship under Grants No. 1256082 and No. 1122374, respectively. Portions of this research also formed part of the senior research thesis of AS while a student at Arizona State University. Since August 2019, CS has been serving as a Program Director in the Di-vision of Mathematical Sciences at the National Science Foundation (NSF), USA, and as a component of this job, he received support from NSF for research, which included work on this paper. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We are indebted to the referee for a careful reading of the manuscript and several comments and suggestions that improved our paper. Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2021.",
year = "2021",
doi = "10.4064/CM7815-2-2020",
language = "English (US)",
volume = "163",
pages = "113--129",
journal = "Colloquium Mathematicum",
issn = "0010-1354",
publisher = "Institute of Mathematics, Polish Academy of Sciences",
number = "1",
}