Mykyta I. Vieprik

activity

20212026

collaborators

4 papers

math.DS2026

Explicit construction of orbit equivalence for rank-one actions

Alexandre I. Danilenko, Mykyta I. Vieprik

Let $G$ be a discrete countable infinite group. Given two rank-one measure-preserving $G$ -actions whose invariant measures are either both finite or both infinite, we give a direct…

math.DS2025

Classification of rank-one actions via the cutting-and-stacking parameters

Alexandre I. Danilenko, Mykyta I. Vieprik

Let $G$ be a discrete countable infinite group. Let $T$ and $T$ be two rank-one $σ$ -finite measure preserving actions of $G$ and let $T$ and $\widetilde {\mathc…

math.DS2024

Rank-one nonsingular actions of countable groups and their odometer factors

Alexandre I. Danilenko, Mykyta I. Vieprik

For an arbitrary countable discrete infinite group $G$ , nonsingular rank-one actions are introduced. It is shown that the class of nonsingular rank-one actions coincides with the c…

math.DS2021

Explicit rank-one constructions for irrational rotations

Alexandre I. Danilenko, Mykyta I. Vieprik

For each {\it well approximable} irrational $θ$ , we provide an explicit rank-one construction of the $e^{2 π i θ}$ -rotation $R_{θ}$ on the circle $T$ . This solves "almost surely" a…