26 citations · 55 across the 25 of their papers we have counts for
35 papers
Explicit construction of orbit equivalence for rank-one actions
Alexandre I. Danilenko, Mykyta I. Vieprik
Let be a discrete countable infinite group. Given two rank-one measure-preserving -actions whose invariant measures are either both finite or both infinite, we give a direct…
Classification of rank-one actions via the cutting-and-stacking parameters
Alexandre I. Danilenko, Mykyta I. Vieprik
Let be a discrete countable infinite group. Let and be two rank-one -finite measure preserving actions of and let and $\widetilde {\mathc…
Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees
Alexandre I. Danilenko, Artem Dudko
Let be a countable branch group of automorphisms of a spherically homogeneous rooted tree. Under some assumption on finitarity of , we construct, for each sequence $ω\in\{0,…
Rank-one nonsingular actions of countable groups and their odometer factors
Alexandre I. Danilenko, Mykyta I. Vieprik
For an arbitrary countable discrete infinite group , nonsingular rank-one actions are introduced. It is shown that the class of nonsingular rank-one actions coincides with the c…
Explicit rank-one constructions for irrational rotations
Alexandre I. Danilenko, Mykyta I. Vieprik
For each {\it well approximable} irrational , we provide an explicit rank-one construction of the -rotation on the circle . This solves "almost surely" a…
Krieger's type for ergodic nonsingular Poisson actions of non-(T) locally compact groups
Alexandre I. Danilenko
It is shown that each non-compact locally compact second countable non-(T) group possesses non-strongly ergodic weakly mixing IDPFT Poisson actions of arbitrary Krieger's type.…