PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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

Volume 230 / 2015

Joanna Kułaga-Przymus Fundamenta Mathematicae 230 (2015), 15-76 MSC: Primary 37A05, 37A10; Secondary 37A30, 37A35. DOI: 10.4064/fm230-1-2


We compare self-joining and embeddability properties. In particular, we prove that a measure preserving flow $(T_t)_{t\in \mathbb {R}}$ with $T_1$ ergodic is $2$-fold quasi-simple (resp. $2$-fold distally simple) if and only if $T_1$ is $2$-fold quasi-simple (resp. $2$-fold distally simple). We also show that the Furstenberg–Zimmer decomposition for a flow $(T_t)_{t\in \mathbb {R}}$ with $T_1$ ergodic with respect to any flow factor is the same for $(T_t)_{t\in \mathbb {R}}$ and for $T_1$. 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.


  • Joanna Kułaga-PrzymusInstitute 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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image