V. Ryzhikov

activity

20112025

most citedHomogeneous spectrum, Disjointness of Convolutions, and Mixing Properties of Dynamical Systems

16 citations · 39 across the 39 of their papers we have counts for

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math.DS2025

Universal Weighted Averaging for Ergodic Flows

Valery V. Ryzhikov

This paper studies homothetic and more general weighted averages for flows. Absolutely continuous convolutions of singular weights are considered, thereby strengthening Kozlov-Tres…

math.DS2025

Continuum pairwise disjoint automorphisms with Lebesgue spectrum

Valery V. Ryzhikov

A continuous family of pairwise disjoint even factors of Gaussian suspensions for Sidon transformations is presented. These factors have the same Lebesgue spectrum, but different K…

math.DS2025★ 1 cited

Slow convergence almost everywhere of ergodic averages

Valery V. Ryzhikov

For an ergodic action of the group $Z^{n}$ on a probability space and a given arbitrarily slowly decreasing to zero sequence, there exists an integrable function such that the standa…

math.DS2025★ 1 cited

Slow convergence of Birkhoff ergodic averages

Valery V. Ryzhikov

Let ${T^{z}}$ be an ergodic action of the group $Z^{n}$ by automorphisms of the probability space $(X, m)$ , $\sum_{i}^{\infty} a_{i} < \infty$ , $a_{i} > 0$ . For any sequence $M_{k} \to + \infty$ th…

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.DS2025

Recurrence of integral zeros for ergodic flows

Valery V. Ryzhikov

Let a flow $T_{t}$ preserve an ergodic probability measure $μ$ , $\int f d μ = 0$ , and $μ (A) > 0$ . Then for almost all $x \in A$ , for which $f (x) \neq = 0$ , there is a sequence ${t_k}\to \inf…