W-measurable sensitivity of semigroup actions

Francisc Bozgan, Anthony Sanchez, Cesar E. Silva, Jack Spielberg, David Stevens, Jane Wang

Research output: Contribution to journalArticlepeer-review

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).

Original languageEnglish (US)
Pages (from-to)113-129
Number of pages17
JournalColloquium Mathematicum
Volume163
Issue number1
DOIs
StatePublished - 2021

Keywords

  • Ergodic
  • Nonsingular transformation
  • Sensitive dependence
  • measure-preserving

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'W-measurable sensitivity of semigroup actions'. Together they form a unique fingerprint.

Cite this