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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.
Joanna Kułaga-Przymus. "On embeddability of automorphisms into measurable flows from the point of view of self-joining properties." Fundamenta Mathematicae 230.1 (2015): 15-76. <http://eudml.org/doc/283271>.
@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 -