16 citations · 51 across the 58 of their papers we have counts for
6 papers · 1 filter
Slow convergences of ergodic averages
Valery V. Ryzhikov
Birkhoff's theorem states that for an ergodic automorphism, the time averages converge to the space average. Given sequence , U. Krengel proved that for any ergodic auto…
Self-joinings and generic extensions of ergodic systems
Valery V. Ryzhikov
We show that typical extensions of ergodic systems inherit the triviality of pairwise independent self-joinings. This property (introduced by A. del Junco and D. Rudolph) is relate…
Generic extensions of ergodic actions
Valery V. Ryzhikov
The article considers generic extensions of measure-preserving actions. We prove that the P-entropy of the generic extensions with finite P-entropy is infinite. This is exploited t…
Tensor-simple spectrum of unitary flows
Valery V. Ryzhikov
Unitary flows of dynamic origin are proposed such that for every countable subset the tensor product has simple spectrum. Th…
Spectra of self-similar ergodic actions
Valery V. Ryzhikov
This note is devoted to infinite self-similar rank 1 constructions and their applications to the spectral theory of dynamical systems. The properties of orthogonal operators induce…
Absolute continuity and singularity of spectra for flows
Valery V. Ryzhikov
Answering the question of V.I. Oseledets, we present a random variable such that the sum has a singular distribution for a set of parameters dense in $(1, +\in…