A. I. Danilenko

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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 $I ¨ $ -finite measure preserving actions of $G$ and let $T$ and $\widetilde {\math…

math.DS2025

Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees

Alexandre I. Danilenko, Artem Dudko

Let $G$ be a countable branch group of automorphisms of a spherically homogeneous rooted tree. Under some assumption on finitarity of $G$ , we construct, for each sequence $Ï\in\{0…