Geodesic
Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows
Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 912-917

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $S$ and $T$ be automorphisms of a probability space whose powers $S \otimes S$ and $T \otimes T$ isomorphic. Are the automorphisms $S$ and $T$ isomorphic? This question of Thouvenot is well known in ergodic theory. We answer this question and generalize a result of Kulaga concerning isomorphism in the case of flows. We show that if weakly mixing flows $S_t \otimes S_t$ and $T_t \otimes T_t$ are isomorphic, then so are the flows $S_t$ and $T_t$, provided that one of them has a weak integral limit.
Keywords: flow with invariant measure, weak closure, tensor power of a dynamical system, metric isomorphism. 
@article{MZM_2018_104_6_a8,
     author = {V. V. Ryzhikov},
     title = {Thouvenot's {Isomorphism} {Problem} for {Tensor} {Powers} of {Ergodic} {Flows}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {912--917},
     publisher = {mathdoc},
     volume = {104},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a8/}
}
TY  - JOUR
AU  - V. V. Ryzhikov
TI  - Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows
JO  - Matematičeskie zametki
PY  - 2018
SP  - 912
EP  - 917
VL  - 104
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a8/
LA  - ru
ID  - MZM_2018_104_6_a8
ER  - 
%0 Journal Article
%A V. V. Ryzhikov
%T Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows
%J Matematičeskie zametki
%D 2018
%P 912-917
%V 104
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a8/
%G ru
%F MZM_2018_104_6_a8
V. V. Ryzhikov. Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows. Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 912-917. http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a8/