We introduce a property of ergodic flows, called Property B. We prove that an ergodic hyperfinite equivalence relation of type III₀ whose associated flow has this property is not of product type. A consequence is that a properly ergodic flow with Property B is not approximately transitive. We use Property B to construct a non-AT flow which-up to conjugacy-is built under a function with the dyadic odometer as base automorphism.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-5,
author = {Maria Joi\c ta and Radu-B. Munteanu},
title = {A property of ergodic flows},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {249-258},
zbl = {06401037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-5}
}
Maria Joiţa; Radu-B. Munteanu. A property of ergodic flows. Studia Mathematica, Tome 223 (2014) pp. 249-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-5/