Related papers: A note on mean equicontinuity

We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with nite local complexity the only equicontinuous systems are then shown to be…

The Hurewicz theorem is a fundamental result in classical dimension theory concerning continuous maps which lower topological dimension. We study whether or not its analogue holds for mean dimension of dynamical systems. Our first main…

We show that the semigroup associated to a second-order elliptic system is positive if and only if the differential equations are essentially decoupled and the coefficients are real-valued. This means the system can be replaced by an…

Let $X$ and $Y$ be topological spaces, let $Z$ be a metric space, and let $f: X\times Y\to Z$ be a mapping. It is shown that when $Y$ has a countable base $\mathcal B$, then under a rather general condition on the set-valued mappings $X\ni…

Let $(X,G)$ be a topological dynamical system, given by the action of a is a countable discrete infinite group on a compact metric space $X$. We prove that if $(X,G)$ is minimal, then it is either diam-mean $m$-equicontinuious or diam-mean…

For an infinite discrete group $G$ acting on a compact metric space $X$, we introduce several weak versions of equicontinuity along subsets of $G$ and show that if a minimal system $(X,G)$ admits an invariant measure then $(X,G)$ is distal…

We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…

This paper is devoted to the investigation of the weighted mean topological dimension in dynamical systems. We show that the weighted mean dimension is not larger than the weighted metric mean dimension, which generalizes the classical…

Let $X$ be a full-shift on the alphabet $[0, 1]^a$ and let $(Y, S)$ be an arbitrary dynamical system. We prove that any equivariant continuous map from $X$ to $Y$ has conditional metric mean dimension not less than $a-\mathrm{mdim}(Y, S)$.…

A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of the Stone-Cech compactification of the natural numbers, or it…

We investigate the existence and regularity of locally invariant manifolds near an approximately invariant set that satisfies a geometric hyperbolicity condition with respect to an abstract ``generalized" dynamical system in Banach spaces.…

By proving the minimality of face transformations acting on the diagonal points and searching the points allowed in the minimal sets, it is shown that the regionally proximal relation of order $d$, $\RP^{[d]}$, is an equivalence relation…

We consider metrizable ergodic topological dynamical systems over locally compact, $\sigma$-compact abelian groups. We study pure point spectrum via suitable notions of almost periodicity for the points of the dynamical system. More…

A subset of a Banach space is called equilateral if the distances between any two of its distinct elements are the same. It is proved that there exist non-separable Banach spaces (in fact of density continuum) with no infinite equilateral…

We prove the existence of measurable invariant manifolds for small perturbations of linear Random Dynamical Systems evolving on a Banach space and admitting a general type of dichotomy, both for continuous and discrete time. Moreover, the…

We introduce the notion of an asymptotically equicontinuous sequence of linear operators, and use it to prove the following result. If $X,Y$ are topological vector spaces, if $T_n,T:X\to Y$ are continuous linear maps, and if $D$ is a dense…

We find necessary and sufficient conditions for a dynamical system to be topologically conjugate to any given substitution minimal system, thus extending the results in [CKL] for the Morse and Toeplitz substitutions.

A Banach space $X$ is said to have property (K) if every $w^*$-convergent sequence in $X^*$ admits a convex block subsequence which converges with respect to the Mackey topology. We study the connection of this property with strongly weakly…

The notion of topological equivalence plays an essential role in the study of dynamical systems of flows. However, it is inherently difficult to generalize this concept to systems without well-posedness in the sense of Hadamard. In this…

On a measure theoretical dynamical system with spectral gap property we consider non-integrable observables with regularly varying tails and fulfilling a mild mixing condition. We show that the normed trimmed sum process of these…