A property of ergodic flows

Maria Joiţa¹ ; Radu-B. Munteanu²

¹ Department of Mathematics Faculty of Applied Sciences University Politehnica of Bucharest 313 Splaiul Independentei 060042 Bucureşti, Romania and Department of Mathematics University of Bucharest 14 Academiei St. 010014 Bucureşti, Romania
² Department of Mathematics University of Bucharest 14 Academiei St. 010014 Bucureşti, Romania

Studia Mathematica, Tome 225 (2014) no. 3, pp. 249-258

Résumé

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.

Détail

DOI : 10.4064/sm225-3-5

Keywords: introduce property ergodic flows called property nbsp prove ergodic hyperfinite equivalence relation type iii whose associated flow has property product type consequence properly ergodic flow property nbsp approximately transitive property nbsp construct non at flow which conjugacy built under function dyadic odometer base automorphism