Valery V. Ryzhikov

activity

20142025

most citedSlow decay of correlations for generic mixing automorphisms

1 citations · 1 across the 19 of their papers we have counts for

collaborators

19 papers

math.DS2025

Slow convergence of ergodic averages for actions of amenable groups

Valery V. Ryzhikov

We show slow convergence of weighted ergodic averages for flows and actions of countable amenable groups.

math.DS2024

Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals

Valery V. Ryzhikov

We recall theorems by Krygin, Atkinson, Shneiberg and propose the following assertion. Let $T_{t}$ be an ergodic flow on $(X, μ)$ , let a function $f$ on $X$ have zero mean, and $μ(A)>…

math.DS2024

Multiple mixing, 75 years of Rokhlin's problem

Valery V. Ryzhikov

In 1949, V.A. Rokhlin introduced new invariants for measure-preserving transformations, called k-fold mixing. Does mixing imply k-fold mixing? -- this problem remains open. We reca…

math.DS2024

Spectra and joint dynamics of Poisson suspensions for rank-one automorphisms

Valery V. Ryzhikov

For every natural $n > 1$ , there is an operator $T$ of dynamical origin such that its tensor power $T^{\otimes n}$ has singular spectrum, and $T^{\otimes (n + 1)}$ has absolutely conti…

math.DS2024

Non-commuting transformations with non-converging 2-fold ergodic averages

Valery V. Ryzhikov

In connection with the results of Tim Austin, and Wen Huang, Song Shao, Xiangdong Ye we present the following assertion: there are infinite automorphisms $S, T$ , some set $A$ of pos…

math.DS2024

Typical infinite mixing automorphisms are rank-one

Valery V. Ryzhikov

Bashtanov proved that generic mixing automorphisms of probability space with respect to the Alpern-Tikhonov metric had rank one. Using Sidon's constructions, we show that generic i…