Geodesic
A property of ergodic flows
Maria Joiţa 1   ; Radu-B. Munteanu 2
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
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

Maria Joiţa  1   ; Radu-B. Munteanu  2

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 
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Maria Joiţa; Radu-B. Munteanu. A property of ergodic flows. Studia Mathematica, Tome 225 (2014) no. 3, pp. 249-258. doi: 10.4064/sm225-3-5

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