26 citations · 38 across the 7 of their papers we have counts for
7 papers
Around Kalikow's theorem on multiple mixing
Valery V. Ryzhikov
Some results in ergodic theory on joinings and multiple mixing and the proof of Steve Kalikow's theorem on 3-fold mixing of 2-fold mixing rank one automorphisms are discussed.
Asymmetry of Entropy Invariants for Generic Mixing -Actions
Mikhail V. Engelgardt, Valery V. Ryzhikov
Suppose that for a mixing -action, , there exists a Kirillov-Kushnirenko entropy that is zero for this action and completely positive for its inverse. We prove that this…
On spectral multiplicities of Gaussian actions
V. V. Ryzhikov
For any set of natural numbers there are mixing Gaussian automorphisms and non-mixing Gaussian automorphisms with singular spectrum (as well as some automorphisms which are dis…
Chacon's Type Ergodic Transformations with Unbounded Arithmetic Spacers
V. V. Ryzhikov
The following generalizations of the Chacon map are proposed: instead of classical constant spacer sequence let a sequence be one with unbounded . (We me…
Weak limits of powers of Chacon's automorphism
Élise Janvresse, A. A. Prikhod'Ko, Thierry De La Rue +1
We completely describe the weak closure of the powers of the Koopman operator associated to Chacon's classical automorphism. We show that weak limits of these powers are the ortho-…
Around King's Rank-One theorems: Flows and Z^n-actions
Élise Janvresse, Thierry De La Rue, Valery Ryzhikov
We study the generalizations of Jonathan King's rank-one theorems (Weak-Closure Theorem and rigidity of factors) to the case of rank-one R-actions (flows) and rank-one Z^n-actions.…
On self-similarities of ergodic flows
Alexandre I. Danilenko, Valery V. Ryzhikov
Given an ergodic flow , let be the set of reals for which the flows and are isomorphic. It is proved that i…