Related papers: Frequently hypercyclic $C_0$-semigroups indexed wi…

We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the…

Let $\{T(t)\}_{t\geq 0}$ be a $C_0$-semigroup of bounded linear operators on the Banach space ${X}$ into itself and let $A$ be their infinitesimal generator. In this paper, we show that if $T(t)$ is uniformly ergodic, then $A$ does not have…

A numerical semigroup $S$ is a cofinite, additively-closed subset of $\mathbb Z_{\ge 0}$ that contains 0, and a factorization of $x \in S$ is a $k$-tuple $z = (z_1, \ldots, z_k)$ where $x = z_1a_1 + \cdots + z_ka_k$ expresses $x$ as a sum…

We investigate rates of decay for $C_0$-semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains the best possible estimate on the rate of decay, that is to…

If $(T_t)$ is a semigroup of Markov operators on an $L^1$-space that admits a non-trivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as $t \to \infty$. In this article we…

A regular operator T on a Hilbert C^*-module is defined just like a closed operator on a Hilbert space, with the extra condition that the range of (I+T^*T) is dense. Semiregular operators are a slightly larger class of operators that may…

Let $X$ be a nonempty set and $\mathcal{P}=\{X_i\colon i\in I\}$ a partition of $X$. Denote by $T(X)$ the full transformation semigroup on $X$, and $T(X, \mathcal{P})$ the subsemigroup of $T(X)$ consisting of all transformations that…

A {\it dynamical system\/} is a pair $(X,\langle T_s\rangle_{s\in S})$, where $X$ is a compact Hausdorff space, $S$ is a semigroup, for each $s\in S$, $T_s$ is a continuous function from $X$ to $X$, and for all $s,t\in S$, $T_s\circ…

In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…

This paper introduces a novel approach to enumerate and assess Trapping sets in quasi-cyclic codes, those with circulant sizes that are non-prime numbers. Leveraging the quasi-cyclic properties, the method employs a tabular technique to…

In this work we consider families of smooth vector fields having a persistent polycycle with $n$ hyperbolic saddles. We derive the asymptotic expansion of the return map associated to the polycycle, determining explicitly its leading terms.…

In this paper we introduce and study the concept of cyclic subgroup commutativity degree of a finite group $G$. This quantity measures the probability of two random cyclic subgroups of $G$ commuting. Explicit formulas are obtained for some…

This paper provides a complete characterization of quasicontractive $C_0$-semigroups on Hardy and Dirichlet space with a prescribed generator of the form $Af=Gf'$. We show that such semigroups are semigroups of composition operators and we…

We show that there exists an invertible $\mathcal{U}$-frequently hypercyclic operator on $\ell^p(\mathbb{N})$ ($1\le p <\infty$) whose inverse is not $\mathcal{U}$-frequently hypercyclic.

A sequence $\{T_n\}_{n=1}^{\infty}$ of bounded linear operators between separable Banach spaces $X, Y$ is called diskcyclic if there exists a vector $x\in X$ such that the disk-scaled orbit $\{\alpha T_n x: n\in \mathbb{N}, \alpha…

Let $\mathcal{H}$ be an infinite dimensional real or complex separable Hilbert space. We introduce a special type of a bounded linear operator $T$ and its important relation with invariant subspace problem on $\mathcal{H}$: operator $T$ is…

Let $S$ and $\Delta$ be numerical semigroups. A numerical semigroup $S$ is an $\mathbf{I}(\Delta)$-{\it semigroup} if $S\backslash \{0\}$ is an ideal of $\Delta$. We will denote by $\mathcal{J}(\Delta)=\{S \mid S \text{ is an…

We study certain dynamical systems which leave invariant an indefinite quadratic form via semigroups or evolution families of complex symmetric Hilbert space operators. In the setting of bounded operators we show that a…

We give a detailed description of infinite locally nilpotent groups G such that the index |C_G (x) : <x>| is finite, for every non-normal cyclic subgroup <x> of G. We are also able to extend our analysis to all non-periodic groups…

The purpose of this paper is to characterize weak supercyclicity for Hilbert-space contractions, which is shown to be equivalent to characterizing weak supercyclicity for unitary operators$.$ This is naturally motivated by an open question…