Related papers: Compact operator semigroups applied to dynamical s…
We present a concise, but systematic, review of the ergodicity issue in strongly correlated systems. After giving a brief historical overview, we analyze the issue within the Green's function formalism by means of the equations of motion…
This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics allows us to extend to higher dimensions a number of…
Among the ergodic actions of a compact quantum group $\mathbb{G}$ on possibly non-commutative spaces, those that are {\it embeddable} are the natural analogues of actions of a compact group on its homogeneous spaces. These can be realized…
We give a characterization of the compact operators on a model space in terms of asymptotic Toeplitz operators.
We obtain Szeg\H o-type limit theorems for Toeplitz operators on the weighted Bergman spaces $A^{2}_{\alpha}(\mathbb{B}^{n})$, and on $L^{2}(G)$, presenting separate formulations for compact and locally compact Abelian groups. Furthermore,…
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…
We completely characterize the mean ergodic composition operators on $H^\infty(\mathbb{B}_n)$. In particular, we show that a composition operator acting on this space is mean ergodic if and only if it is uniformly mean ergodic.
In \cite{BAMU}, an ergodic theorem \`a la Birkhoff-von Neumann for the action of the fundamental group of a compact negatively curved manifold on the boundary of its universal cover is proved. A quick corollary is the irreducibility of the…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…
This paper investigates the ergodicity of Markov--Feller semigroups on Polish spaces, focusing on very weak regularity conditions, particularly the Ces\`aro eventual continuity. First, it is showed that the Ces\`aro average of such…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…
We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…
In this article, we consider actions of \mathcal{Z}_+^d, \mathcal{R}_+^d and finitely generated free groups on a von Neumann algebras $M$ and prove a version of maximal ergodic inequality. Additionally, we establish non-commutative…
In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…
We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with a separable dual.
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are…
The purpose of this paper is to give an updated survey on various algebraic and analytic properties of semigroups related to fixed point properties of semigroup actions on a non-empty closed convex subset of a Banach space or, more…