We compare self-joining and embeddability properties. In particular, we prove that a measure preserving flow 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 with T₁ ergodic with respect to any flow factor is the same for 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-1-2,
author = {Joanna Ku\l aga-Przymus},
title = {On embeddability of automorphisms into measurable flows from the point of view of self-joining properties},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {15-76},
zbl = {06419991},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-1-2}
}
Joanna Kułaga-Przymus. On embeddability of automorphisms into measurable flows from the point of view of self-joining properties. Fundamenta Mathematicae, Tome 228 (2015) pp. 15-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-1-2/