Related papers: Non-removable term ergodic action semigroups/group…
Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the…
In this note we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces, and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property then…
We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of…
We construct examples of minimal and uniquely ergodic systems realizing all possible behaviors in the interplay of measurable and topological nilfactors. To build such examples, we adapt an idea that stems from Furstenberg's construction of…
In this note we show existence of bounded, transitive cocycles over a transitive action of a finitely generated group, and bounded, ergodic cocycles over an ergodic, probability preserving action of $\Bbb Z^d$.
Pugh and Shub have conjectured that essential accessibility implies ergodicity, for a $C^2$, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satsified by all…
We consider semigroups of Ruelle-expanding maps, parameterized by random walks on the free semigroup, with the aim of examining their complexity and exploring the relation between intrinsic properties of the semigroup action and the…
The aim of this article is to prove that the Torelli group action on the G-character varieties is ergodic for G a connected, semi-simple and compact Lie group.
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…
For operators defined on locally convex spaces we define the notions of boundedness and ergodicity associated to an infinite matrix. Given two matrices $ A$ and $ B$, we study when $ A$-bounded operators are $ B$-ergodic. Using this…
We consider skew product extension of irrational rotations on the circle by $\Z^2$ determined by an integer valued function as well as a fixed point on the circle. We study ergodic components of such extension.
We establish criteria for turbulence in certain spaces of C*-algebra representations and apply this to the problem of nonclassifiability by countable structures for group actions on a standard atomless probability space (X,\mu) and on the…
We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation…
In this article we discuss relations between algebraic and dynamical properties of non-cyclic semigroups of rational maps.
In a couple of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In this article, we introduce and examine…
These notes are a self-contained introduction to the use of dynamical and probabilistic methods in the study of hyperbolic groups. Most of this material is standard; however some of the proofs given are new, and some results are proved in…
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
In this paper, we introduce the notions of topological pressure and measure-theoretic entropy for a free semigroup action. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a…
This paper presents a rigorous treatment of the concept of extensivity in equilibrium thermodynamics from a geometric point of view. This is achieved by endowing the manifold of equilibrium states of a system with a smooth atlas that is…
Ergodic and combinatorial results obtained in [10] involved measure preserving actions of the affine group ${\mathcal A}_K$ of a countable field $K$. In this paper we develop a new approach based on ultrafilter limits which allows one to…