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## Fundamenta Mathematicae

2015 | 230 | 1 | 15-76
Tytuł artykułu

### On embeddability of automorphisms into measurable flows from the point of view of self-joining properties

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We compare self-joining and embeddability properties. In particular, we prove that a measure preserving flow $(T_t)_{t∈ℝ}$ with T₁ ergodic is 2-fold quasi-simple (resp. 2-fold distally simple) if and only if T₁ is 2-fold quasi-simple (resp. 2-fold distally simple). We also show that the Furstenberg-Zimmer decomposition for a flow $(T_t)_{t∈ℝ}$ with T₁ ergodic with respect to any flow factor is the same for $(T_t)_{t∈ℝ}$ and for T₁. We give an example of a 2-fold quasi-simple flow disjoint from simple flows and whose time-one map is simple. We describe two classes of flows (flows with minimal self-joining property and flows with the so-called Ratner property) whose time-one maps have unique embeddings into measurable flows. We also give an example of a 2-fold simple flow whose time-one map has more than one embedding.
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Tom
Numer
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15-76
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wydano
2015
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• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland
• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
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