Let G be a non-periodic amenable group. We prove that there does not exist a topological
action of G for which the set of ergodic invariant measures coincides with the set of all …

We prove that a generic probability measure-preserving (pmp) action of a countable
amenable group G has scaling entropy that cannot be dominated by a given rate of growth …

Relative uniformly positive entropy of induced amenable group actions Page 1 Ergod. Th. &
Dynam. Sys., (2024), 44, 569–593 © The Author(s), 2023. Published by Cambridge University …

This paper deals with the problem of finding the range of entropy values resulting from
actions of discrete amenable groups by automorphisms of compact abelian groups. When …

Let $ G $ be a discrete countable infinite group that does not have Kazhdan's property (T)
and let $\kappa $ be a generating probability measure on $ G $. Then for each $ t> 0$, there …

We establish a new characterization of property (T) in terms of the Furstenberg entropy of
nonsingular actions. Given any generating measure $\mu $ on a countable group $ G $, A …

We prove that every dynamical system $ X $ with free action of a countable amenable group
$ G $ by homeomorphisms has a zero-dimensional extension $ Y $ which is faithful and …

We study an invariant of dynamical systems called naive entropy, which is defined for both
measurable and topological actions of any countable group. We focus on nonamenable …

We prove that an ergodic free action of a countable discrete amenable group with
completely positive entropy has a countable Lebesgue spectrum. Our approach is based on …

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin
entropy (or, less generally, positive sofic entropy), then it factors onto all Bernoulli shifts of …