A property of ergodic flows
Volume 225 / 2014
Studia Mathematica 225 (2014), 249-258
MSC: Primary 37A20; Secondary 37A35, 37A40, 46L10.
DOI: 10.4064/sm225-3-5
Abstract
We introduce a property of ergodic flows, called Property B. We prove that an ergodic hyperfinite equivalence relation of type III$_{0}$ 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.
