Related papers: Sofic mean dimension

We introduce the notion of dynamical metric order of a continuous map on a compact metric space, study its basic properties, and compute it for several classes of maps. This concept which is a counterpart of the metric mean dimension with…

We show for a free action of a countable group $\Gamma$ on a finite-dimensional, compact metric space by homeomorphisms that the dynamic asymptotic dimension is either infinite or coincides with the asymptotic dimension of $\Gamma$.

We examine several definitions of soficity for monoids obtained by generalizing various definitions of sofic groups. They are not all equivalent and include the definition recently introduced by Ceccherini-Silberstein and Coornaert. One of…

Let $\Gamma$ be a sofic group with a copy of $\mathbb{Z}$ in its center. We construct an uncountable family of pairwise nonisomorphic measure-preserving $\Gamma$ actions with completely positive entropy, none of which is a factor of a…

In this paper, we shall introduce $h$-expansiveness and asymptotical $h$-expansiveness for actions of sofic groups. By the definitions, each $h$-expansive action of sofic groups is asymptotically $h$-expansive. We show that each expansive…

In this thesis, we study the existence of universal objets of two differents types in the theory of topological groups and theirs actions on compacts spaces. In the first part, we contribute to the problem of existence of test spaces for…

The aim of the article is to provide a characterization of the Haagerup property for locally compact, second countable groups in terms of actions on $\sigma$-finite measure spaces. It is inspired by the very first definition of amenability,…

We introduce the Solecki submeasure $\sigma(A)=\inf_F\sup_{x,y\in G}|F\cap xAy|/|F|$ and its left and right modifications on a group $G$, and study the interplay between the Solecki submeasure and the Haar measure on compact topological…

We define the concept of continuum wise expansive for flows, and we prove that continuum wise expansive flows on compact metric spaces with topological dimension greater than one have positive entropy.

We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform…

Dan Rudolph showed that for an amenable group $\Gamma$, the generic measure-preserving action of $\Gamma$ on a Lebesgue space has zero entropy. Here this is extended to nonamenable groups. In fact, the proof shows that every action is a…

The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying…

We construct analoga of Gromov-Hausdorff space for Lorentzian distances and show a Gromov precompactness result for one of them. After calculating the Dushnik-Miller dimension of Minkowski spaces (of manifold dimension larger than 2) to be…

In the context of (not necessarily minimal) actions, we consider the mean diameter and use it to characterize regular factor maps. Building on this characterization, we prove that an action is diam-mean equicontinuous if and only if it is a…

We solve the question of the existence of a Poisson-Pinsker factor for conservative ergodic infinite measure preserving action of a countable amenable group by proving the following dichotomy: either it has totally positive Poisson entropy…

We provide a sufficient condition for a topological partial action of a Hausdorff group on a metric space is continuous, provide that it is separately continuous.

In this paper we extend the definitions of mean dimension and metric mean di-mension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean…

Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type III$_\lambda, 0 < \lambda < 1$. Winsl{\o}w's fundamental homomorphism is a complete invariant. This…

We define the notion of entropy for a cross section of an action of continuous amenable group and relate it to the entropy of the ambient action. As a result, we are able to answer a question of J.P. Thouvenot about completely positive…

Coxeter groups admit amenable actions on compact spaces. Moreover, they have finite asymptotic dimension.