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

@article{JoannaKułaga2015,
abstract = {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.},
author = {Joanna Kułaga-Przymus},
journal = {Fundamenta Mathematicae},
keywords = {joinings; quasi-simplicity; distal simplicity; embeddability; uniqueness of embedding},
language = {eng},
number = {1},
pages = {15-76},
title = {On embeddability of automorphisms into measurable flows from the point of view of self-joining properties},
url = {http://eudml.org/doc/283271},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Joanna Kułaga-Przymus
TI - On embeddability of automorphisms into measurable flows from the point of view of self-joining properties
JO - Fundamenta Mathematicae
PY - 2015
VL - 230
IS - 1
SP - 15
EP - 76
AB - 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.
LA - eng
KW - joinings; quasi-simplicity; distal simplicity; embeddability; uniqueness of embedding
UR - http://eudml.org/doc/283271
ER -