相关论文: Construction of minimal skew products of amenable …

We show that every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite. As a consequence, the crossed products of minimal such actions are…

We explore classifiability of crossed products of actions of countable amenable groups on compact, metrizable spaces. It is completely understood when such crossed products are simple, separable, unital, nuclear and satisfy the UCT: these…

We discuss some techniques related to equivariant compactifications of uniform spaces and amenability of topological groups. In particular, we give a new proof of a recent result by Glasner and Weiss describing the universal minimal flow of…

We study amenable minimal Cantor systems of free groups arising from the diagonal actions of the boundary actions and certain Cantor systems. It is shown that every virtually free group admits continuously many amenable minimal Cantor…

Given a minimal action $G\curvearrowright X$ of a countable group $G$ on a compact space $X$, we prove that if the reduced crossed product $G\ltimes_rC(X)$ is simple, then there exists a point whose stabilizer subgroup has trivial amenable…

We show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison. This class includes all nonamenable hyperbolic groups, many HNN-extensions, nonamenable…

We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…

A space is called minimal if it admits a minimal continuous selfmap. We give examples of metrizable continua $X$ admitting both minimal homeomorphisms and minimal noninvertible maps, whose squares $X\times X$ are not minimal, i.e., they…

Let $\alpha: G\curvearrowright X$ be a continuous action of an infinite countable group on a compact Hausdorff space. We show that, under the hypothesis that the action $\alpha$ is topologically free and has no $G$-invariant regular Borel…

We define and study notions of amenability and skew-amenability of continuous actions of topological groups on compact topological spaces. Our main motivation is the question under what conditions amenability of a topological group passes…

The following well known open problem is answered in the negative: Given two compact spaces $X$ and $Y$ that admit minimal homeomorphisms, must the Cartesian product $X\times Y$ admit a minimal homeomorphism as well? A key element of our…

Let $X$ be an infinite compact metric space with finite covering dimension and let $\alpha, \beta : X\to X$ be two minimal homeomorphisms. We prove that the crossed product $C^*$-algebras $C(X)\rtimes_\alpha\Z$ and $C(X)\rtimes_\belta\Z$…

We introduce the notion of tracial amenability for actions of discrete groups on unital, tracial C$^*$-algebras, as a weakening of amenability where all the relevant approximations are done in the uniform trace norm. We characterize tracial…

We establish several new characterizations of amenable $W^*$- and $C^*$-dynamical systems over arbitrary locally compact groups. In the $W^*$-setting we show that amenability is equivalent to (1) a Reiter property and (2) the existence of a…

We prove a structure theorem for topologically conservative real skew product extensions of distal minimal compact metric $\Z$-flows. The main result states that every such extension can be represented by a perturbation of a Rokhlin skew…

We show that a relatively ergodic extension of measure-preserving dynamical systems has relative discrete spectrum if and only if it can be represented as a skew-product by a bundle of compact homogeneous spaces. Our result holds without…

Let $G$ be a locally compact Polish group. A metrizable $G$-flow $Y$ is called model-universal if by considering the various invariant probability measures on $Y$, we can recover every free action of $G$ on a standard Lebesgue space up to…

We will show that any extension of a product of two Cantor minimal $\Z$-systems is affable in the sense of Giordano, Putnam and Skau.

We prove a structure theorem for topologically recurrent real skew product extensions of distal minimal compact metric flows with a compactly generated Abelian acting group (e.g. $\Z^d$-flows and $\R^d$-flows). The main result states that…

We study Smale skew product endomorphisms (introduced in [27]) now over countable graph directed Markov systems, and we prove the exact dimensionality of conditional measures in fibers, and then the global exact dimensionality of the…