Related papers: Chaotic behavior of group actions

Let $X$ be a Hausdorff topological group and $G$ a locally compact subgroup of $X$. We show that $X$ admits a locally finite $\sigma$-discrete $G$-functionally open cover each member of which is $G$-homeomorphic to a twisted product…

In this paper, we first prove that the topological entropy of induced map of any distal homeomorphism of a compact metric space is null. Then we consider induced map $2^f$ of an arbitrary pointwise periodic homeomorphism $f:X\to X$ of a…

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…

In this work, we study pmp actions of countable groups on arbitrary diffuse probability spaces under the point of view of weak equivalence. We will show that any such an action is weakly equivalent to an action on a standard probability…

We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$-action has been considered on a strongly monotone skew-product semiflow. Here we relax the…

Let $K$ be a compact metrizable group and $\Ga$ be a group of automorphisms of $K$. We first show that each $\ap \in \Ga$ is distal on $K$ implies $\Ga$ itself is distal on $K$, a local to global correspondence provided $\Ga$ is a…

We consider the class of countable groups possessing an action on a finite product of hyperbolic graphs where every infinite order element acts loxodromically. When the graphs are locally finite, we obtain strong structure theorems for the…

For an arbitrary countable discrete infinite group $G$, nonsingular rank-one actions are introduced. It is shown that the class of nonsingular rank-one actions coincides with the class of nonsingular $(C,F)$-actions. Given a decreasing…

We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris-Nickolas for…

Recently, in connection with C*-algebra theory, the first author and Danilo Royer introduced ultragraph shift spaces. In this paper we define a family of metrics for the topology in such spaces, and use these metrics to study the existence…

In his work on the Farrell-Jones Conjecture, Arthur Bartels introduced the concept of a "finitely $\mathcal{F}$-amenable" group action, where $\mathcal{F}$ is a family of subgroups. We show how a finitely $\mathcal{F}$-amenable action of a…

In this work, we will introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random groups under an additional dimension condition on the volume of…

We study the automorphism groups of countable homogeneous directed graphs (and some additional homogeneous structures) from the point of view of topological dynamics. We determine precisely which of these automorphism groups are amenable…

We study topological groups $G$ for which the universal minimal $G$-system $M(G)$, or the universal irreducible affine $G$-system $IA(G)$ are tame. We call such groups intrinsically tame and convexly intrinsically tame. These notions are…

For a discrete metric space (or more generally a large scale space) $X$ and an action of a group $G$ on $X$ by coarse equivalences, we define a type of coarse quotient space $X_G$, which agrees up to coarse equivalence with the orbit space…

Reid-Smith recently parametrised groups acting on trees with Tits' independence property (P) using graph-based combinatorial structures known as local action diagrams. Properties of the acting (topological) group, such as being locally…

We show that any action of a finite group on a finitely presentable group arises as the action of the group of self-homotopy equivalences of a space on its fundamental group. In doing so, we prove that any finite connected (abstract)…

All sigma-compact, locally compact groups acting sharply n-transitively and continuously on compact spaces M have been classified, except for n=2,3 when M is infinite and disconnected. We show that no such actions exist for n=2 and that…

In this paper, we introduce the notions of lowerable, D-lowerable, P-lowerable, hereditarily lowerable, and hereditarily uniformly lowerable for countably infinite amenable group actions. We show that a system with finite entropy is…

A continuous action of a group G on a compact metric space has sensitive dependence on initial conditions if there is a number e>0 such that for any open set U we can find g in G such that g.U has diameter greater than e. We prove that if a…