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

• Autorzy: Joanna Kułaga-Przymus
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A30: Ergodic theorems, spectral theory, Markov operators
• 37A10: One-parameter continuous families of measure-preserving transformations
• 37A05: Measure-preserving transformations
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 230
• Numer: 1
• Strony: 15-76

Daty

wydano

2015

Twórcy

autor

Joanna Kułaga-Przymus

• 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

Identyfikatory

DOI

10.4064/fm230-1-2