�ber Wurzeln ergodischer Transformationen

Krengel, Ulrich; Michel, H.

doi:10.1007/bf01111449

Cited by 7 publications

(4 citation statements)

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“…In the discrete spectrum case this is also sufficient. These results were later generalized in various ways -both in the discrete [42,5,39,61] and quasi-discrete spectrum [30,50,51,52] case. They include necessary and sufficient conditions for the existence of roots and for the existence of embedding into a flow in the discrete and quasi-discrete spectrum case.…”

Section: Embeddabilitymentioning

confidence: 99%

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

Kułaga-Przymus¹

2015

Fund. Math.

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We compare self-joining-and embeddability properties. In particular, we prove that a measure preserving flow (Tt) t∈R with T1 ergodic is 2-fold quasi-simple (2-fold distally simple) if and only if T1 is 2-fold quasisimple (2-fold distally simple). We also show that the Furstenberg-Zimmer decomposition for a flow (Tt) t∈R with T1 ergodic with respect to any flow factor is the same for (Tt) 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.

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Section: Embeddabilitymentioning

confidence: 99%

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

Kułaga-Przymus¹

2015

Fund. Math.

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“…Ornstein [8] has shown that when T is a Bernoulli automorphism, A can be taken to be the whole real axis. If T is ergodic and has discrete spectrum, Krengel and Michel [7] have shown that there is a 'maximal' flow containing T, whose parameter set A is a certain subgroup of the additive group of the rationals, containing 1. An automorphism S is said to be an rth root of T if S' is isomorphic to T (r = 2,3, ... ).…”

Section: Introductionmentioning

confidence: 99%

“…Halmos's original results have been generalised by Krengel and Michel. Theorem 1.6 [7]. Let T be ergodic, have discrete spectrum and 1 be the only rth root of unity contained in u(T).…”

Section: Introductionmentioning

confidence: 99%