Related papers: Non-ergodic actions, cocycles and superrigidity

Rigid actions have zero Rokhlin entropy and nonpositive sofic entropy. Because rigidity is a stable orbit-equivalence invariant, this provides the first example of an essentially free, ergodic, probability-measure-preserving action of the…

In this paper we study rigidity properties of abelian \hyphenation{break-able}actions with weak or no hyperbolicty. We introduce a general strategy for proving $C^\infty$ local rigidity of algebraic actions. As a consequence, we show…

We discuss properties of orbits of (semi)group actions on locally compact groups G. In particular, we show that if a compactly generated locally compact abelian group acts distally on G then the closure of each of its orbits is a minimal…

Let G be a cyclic group of order 3, 5 or 7, and X=E(n) be the relatively minimal elliptic surface with rational base. In this paper, we prove that under certain conditions on n, there exists a locally linear G-action on X which is…

We pursue the study of local index theory for operators of Fourier-integral type associated to non-proper and non-isometric actions of Lie groupoids, initiated in a previous work. We introduce the notion of geometric cocycles for Lie…

We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many…

In this paper The Ergodic Hypothesis is proven for one class of functions defined in the infinite dimensional unite cube where is given an action of some semigroup of mappings without the condition on metric transitivity. The result has not…

We investigate Gaussian actions through the study of their crossed-product von Neumann algebra. The motivational result is Chifan and Ioana's ergodic decomposition theorem for Bernoulli actions (Ergodic subequivalence relations induced by a…

The notion of compact quantum subgroup is revisited and an alternative definition is given. Induced representations are considered and a Frobenius reciprocity theorem is obtained. A relationship between ergodic actions of compact quantum…

This paper deals with measurable stationary symmetric stable random fields indexed by R^d and their relationship with the ergodic theory of nonsingular R^d-actions. Based on the phenomenal work of Rosinski(2000), we establish extensions of…

We prove a cocycle superrigidity theorem for a large class of coinduced actions. In particular, if $\Lambda$ is a subgroup of a countable group $\Gamma$, we consider a probability measure preserving action $\Lambda\curvearrowright X_0$ and…

We investigate analogues of some of the classical results in homogeneous dynamics in non-linear setting. Let $G$ be a closed subgroup of the group of automorphisms of a biregular tree and $\Gamma<G$ a discrete subgroup. For a large class of…

We extend Dye's reconstruction theorem, which classifies isomorphisms between full groups, to a classification of homomorphisms between full groups. For full groups of ergodic p.m.p. equivalence relations, our result roughly says that such…

We study cocycles of countable groups $\Gamma$ of Borel automorphisms of a standard Borel space $(X, \mathcal{B})$ taking values in a locally compact second countable group $G$. We prove that for a hyperfinite group $\Gamma$ the subgroup of…

We prove that every ergodic amenable action of an algebraic group over a local field of characteristic zero is induced from an ergodic action of an amenable subgroup.

We study polar actions with horizontal sections on the total space of certain principal bundles $G/K\to G/H$ with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we…

If a nontrivial finite group coacts on a graded noetherian down-up algebra $A$ inner faithfully and homogeneously, then the fixed subring is not isomorphic to $A$. Therefore graded noetherian down-up algebras are rigid with respect to…

Classical ergodic theory deals with measure (or measure class) preserving actions of locally compact groups on Lebesgue spaces. An important tool in this setting is a theorem of Mackey which provides spatial models for Boolean G-actions. We…

We study expressive power of continuous logic in classes of metric groups defined by properties of their actions. For example we consider properties non-OB, non-FH and non-FR. The paper substantially extends Section 2 of the paper A.Ivanov,…

Let $G$ be a connected simple Lie group of real rank one and finite center, and let $K$ be a maximal compact subgroup. We study the families of spherical, ball, and uniform averages $(\sigma_t)_{t>0}$, $(\beta_t)_{t>0}$, and $(\mu_t)_{t>0}$…