Related papers: Measure conjugacy invariants for actions of counta…

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of…

It was proved by Brudno that entropy and Kolmogorov complexity for dynamical systems are tightly related. We generalize his results to the case of arbitrary computable amenable group actions. Namely, for an ergodic shift-action, the…

The aim of this paper is to prove ergodic decomposition theorems for probability measures quasi-invariant under Borel actions of inductively compact groups (Theorem 1) as well as for sigma-finite invariant measures (Corollary 1). For…

Let $\Gamma$ be a sofic group, $\Sigma$ be a sofic approximation sequence of $\Gamma$ and $X$ be a $\Gamma$-subshift with nonnegative sofic topological entropy with respect to $\Sigma$. Further assume that $X$ is a shift of finite type, or…

This paper studies the notion of W-measurable sensitivity in the context of semigroup actions. W-measurable sensitivity is a measurable generalization of sensitive dependence on initial conditions. In 2012, Grigoriev et. al. proved a…

This paper is aim to extend Kenneth R. Berg's findings on the maximal entropy theorem and the ergodicity of measure convolution to the case of surjective homomorphisms. We further explores dynamical systems under surjective homomorphism in…

In this short note we construct two countable, infinite conjugacy class groups which admit free, ergodic, probability measure preserving orbit equivalent actions, but whose group von Neumann algebras are not (stably) isomorphic.

Building on work of Popa, Ioana, and Epstein--T\"{o}rnquist, we show that, for every nonamenable countable discrete group $\Gamma$, the relations of conjugacy, orbit equivalence, and von Neumann equivalence of free ergodic (or weak mixing)…

To any positive contraction $Q$ on $\ell^2(W)$, there is associated a determinantal probability measure ${\mathbf P}^Q$ on $2^W$, where $W$ is a denumerable set. Let $\Gamma$ be a countable sofic finitely generated group and $G = (\Gamma,…

Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we…

We prove that if two topologically free and entropy regular actions of countable sofic groups on compact metrizable spaces are continuously orbit equivalent, and each group either (i) contains a w-normal amenable subgroup which is neither…

We prove that for a measure preserving action of a sofic group with positive sofic entropy, the set of points with finite stabilizer have positive measure. This extends results of Weiss and Seward for amenable groups and free groups,…

The paper offers a thorough study of multiorders and their applications to measure-preserving actions of countable amenable groups. By a~{\em multiorder} on a~countable group we mean any probability measure $\nu$ on the collection…

We study periodic points and finitely supported invariant measures for continuous semigroup actions. Introducing suitable notions of periodicity in both topological and measure-theoretical contexts, we analyze the space of invariant Borel…

We continue our study of the outer Pinsker factor for probability measure-preserving actions of sofic groups. Using the notion of doubly quenched convergence developed by Austin, we prove that in many cases the outer Pinsker factor of a…

We prove that if $G$ is a countably infinite group and $(L, \lambda)$ and $(K, \kappa)$ are probability spaces having equal Shannon entropy, then the Bernoulli shifts $G \curvearrowright (L^G, \lambda^G)$ and $G \curvearrowright (K^G,…

Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…

A group is surjunctive if every injective cellular automaton on it is also surjective. Gottschalk famously conjectured that all groups are surjunctive. This remains a central open problem in symbolic dynamics and descriptive set theory.…

We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving actions of countable groups introduced in the previous paper. We prove that every free ergodic action with finite Rokhlin entropy admits…

A countable group G is called k-linear sofic (for some 0 <k \le 1) if finite subsets of G admit "approximate representations" by complex invertible matrices in the normalized rank metric, so that non-identity elements are k-away from the…