Related papers: Orbits of Distal Actions on Locally Compact Groups

Let $G$ be a Lie group acting properly on a smooth manifold $M$. If $M/G$ is connected, then we exhibit some simple and basic constructions for proper actions. In particular, we prove that the reduction principle in compact transformation…

We study the action of a real reductive group $G$ on a Kahler manifold $Z$ which is the restriction of a holomorphic action of a complex reductive Lie group $U^\mathbb{C}.$ We assume that the action of $U$, a maximal compact connected…

Let $G$ be a totally disconnected, locally compact group and let $H$ be a virtually flat (for example, polycyclic) group of automorphisms of $G$. We study the structure of, and relationships between, various subgroups of $G$ defined by the…

Let $(\phi_t)_{t \geq 0}$ be a semigroup of holomorphic functions in the unit disk $\mathbb{D}$ and $K$ a compact subset of $\mathbb{D}$. We investigate the conditions under which the backward orbit of $K$ under the semigroup exists.…

We introduce and study the notion of continuous orbit equivalence of actions of countable discrete groups on Cartan pairs in (twisted) groupoid context. We characterize orbit equivalence of actions in terms of the corresponding…

We show that the topological rank of an orbit full group generated by an ergodic, probability measure-preserving free action of a non-discrete unimodular locally compact Polish group is two. For this, we use the existence of a cross section…

Let $G$ be a connected Lie group and $\text{Sub}_G$ be the space of closed subgroups of $G$ equipped with the Chabauty topology. In this article, we investigate the existence of invariant random subgroups of $G$ supported on various orbits…

We consider partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. In the first part of the paper, we show local differentiable rigidity for such…

We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the \beta-compactification of G (which is a G-space in a natural way), and their minimal closed…

Group actions on a Smale space and the actions induced on the C*-algebras associated to such a dynamical system are studied. We show that an effective action of a discrete group on a mixing Smale space produces a strongly outer action on…

If $G$ is a locally compact group, $CD(G)$ the algebra of convolution dominated operators on $L^2(G)$ then an important question is: Is $\mathbb{C}1+CD(G)$ (respectively $CD(G)$ if $G$ is discrete) inverse-closed in the bounded operators on…

In this work, we study minimal equicontinuous actions which are locally quasi-analytic. The first main result shows that for minimal equicontinuous actions which are locally quasi-analytic, continuous orbit equivalence of the actions…

Given a C*-algebra A with a left action of a locally compact quantum group G on it and a unitary 2-cocycle Omega on \hat G, we define a deformation A_Omega of A. The construction behaves well under certain additional technical assumptions…

Let $T$ be a compact fibered $3$--manifold, presented as a mapping torus of a compact, orientable surface $S$ with monodromy $\psi$, and let $M$ be a compact Riemannian manifold. Our main result is that if the induced action $\psi^*$ on…

We consider continuous extensions of minimal rotations on a locally connected compact group X by arbitrary locally compact Lie groups and prove regularity (i.e. the existence of orbit closures which project onto the whole basis X) in…

Let $G$ be a locally compact abelian group and $\Lambda$ be a closed subgroup of the dual group $\widehat{G}$. In this paper, we investigate modulation preserving operators with respect to $\Lambda$, and give a characterization of them in…

We construct affine uniformly Lipschitz actions on $\ell^1$ and $L^1$ for certain groups with hyperbolic features. For acylindrically hyperbolic groups, our actions have unbounded orbits, while for residually finite hyperbolic groups and…

We give a characterization of hypercyclic using (locally hypercyclic) of semigroup G of affine maps of C^n. We prove the existence of a G-invariant open subset of C^n in which any locally hypercyclic orbit is dense in C^n.

We characterise the groupoid $C^*$-algebras associated to the transformation groupoids of injective actions of discrete countable Ore semi-groups on compact topological spaces in terms of the reduced crossed product from the dual actions,…

We prove that a connected locally compact median space of finite rank which admits a transitive action is isometric to $\mathbb{R}^n$ endowed with the $\ell^1$-metric. In the other side, replacing the transitivity assumption on the group of…