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We apply the (C, F )-construction from [Da] to produce a number of funny rank one infinite measure preserving actions of Abelian groups G with “unusual” multiple recurrence properties. In particular, we construct the following for each p ∈ N ∪ {∞}: (i) a p-recurrent action T = (Tg)g∈G such that (if p 6=∞) no one transformation Tg is (p + 1)-recurrent for… (More)

Glossary 1 1. Definition of the subject and its importance 2 2. Basic Results 2 3. Panorama of Examples 8 4. Mixing notions and multiple recurrence 10 5. Topological group Aut(X,μ) 13 6. Orbit theory 15 7. Smooth nonsingular transformations 21 8. Spectral theory for nonsingular systems 22 9. Entropy and other invariants 25 10. Nonsingular Joinings and… (More)

Using techniques related to the (C,F )-actions we construct explicitly mixing rank-one (by cubes) actions T of G = Rd1 ×Zd2 for any pair of non-negative integers d1, d2. It is also shown that h(Tg) = 0 for each g ∈ G.

- Alexandre I. Danilenko, Valery V. Ryzhikov
- 2009

We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset E ⊂ N as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing… (More)

Let X and Y be Polish spaces with non-atomic Borel measures μ and ν of full support. Suppose that T and S are ergodic non-singular homeomorphisms of (X, μ) and (Y, ν) with continuous Radon-Nikodym derivatives. Suppose that either they are both of type III1 or that they are both of type IIIλ, 0 < λ < 1 and, in the IIIλ case, suppose in addition that both… (More)

- Alexandre I. Danilenko
- Pediatrii︠a︡ akusherstvo i ginekologii︠a︡
- 1967

- Alexandre I. Danilenko, Valery V. Ryzhikov
- 2009

Each subset E ⊂ N is realized as the set of essential values of the multiplicity function for the Koopman operator of an ergodic conservative infinite measure preserving transformation.

It is shown that if E is any subset of N such that either 1 ∈ E or 2 ∈ E then there is a mixing transformation whose set of spectral multiplicities is E.

- Alexandre I. Danilenko, Cesar E. Silva
- Encyclopedia of Complexity and Systems Science
- 2009

- Elena Kalashnikova, Alexandre I. Danilenko
- Arkhiv patologii
- 1985

One hundred and thirty-one structurally different placentas during multifoetal pregnancy have been studied by the morphohistochemical and morphological methods. A high degree of conservation of placenta tissue structures of twins is observed in clinically normal pregnancy; the disorganisation is very mild, and the whole tissue, especially the margin, is… (More)