Related papers: Recurrence properties of hypercyclic operators

We introduce the notion of characteristic functions for commuting tuples of hypercontractions on Hilbert spaces, as a generalization of the notion of Sz.-Nagy and Foias characteristic functions of contractions. We present an explicit method…

We prove the existence of common hypercyclic, entire functions for certain uncountable families of traslation type operators with relative large gaps.

Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…

The kinematical rotations of N-partical Hyperspherical basis are considered. The recurrence relation method of determination of transformation coefficients for arbitrary N-values is demonstrated.

We study the dynamical behaviour of weighted backward shift operators defined on sequence spaces over a directed tree. We provide a characterization of chaos on very general Fr\'echet sequence spaces in terms of the existence of a large…

Let $H(\mathbb{C})$ be the set of all entire functions endowed with the topology of uniform convergence on compact sets. Let $\lambda,b\in\mathbb{C}$, let $C_{\lambda,b}:H(\mathbb{C})\to H(\mathbb{C})$ be the composition operator…

A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…

We study the cyclic and supercyclic dynamical properties of weighted composition operators on the Fock space $\mathcal{F}_2$. A complete characterization of cyclicity which depends on the derivative of the symbol for the composition…

Given a Furstenberg family $\mathscr{F}$ of subsets of $\mathbb{N}$, an operator $T$ on a topological vector space $X$ is called $\mathscr{F}$-transitive provided for each non-empty open subsets $U$, $V$ of $X$ the set $\{n\in \mathbb{Z}_+…

We investigate a generalization of weighted shifts where each weight $w_k$ is replaced by an operator $T_k$ going from a Banach space $X_k$ to another one $X_{k-1}$. We then look if the obtained shift operator $B_{(T_k)}$ defined on the…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We consider the recurrence and transience problem for a time-homogeneous Markov chain on the real line with transition kernel $p(x,\mathrm{d}y)=f_x(y-x)\,\mathrm{d}y$, where the density functions $f_x(y)$, for large $|y|$, have a power-law…

We exclude the existence of frequently hypercyclic operators that have a spectrum contained in the closed unit disc and that intersects the unit circle in only finitely many points under certain additional conditions. This extends a result…

We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…

Frequent hypercyclicity for translation $C_0$-semigroups on weighted spaces of continuous functions is investigated. The results are achieved by establishing an analogy between frequent hypercyclicity for the translation semigroup and for…

We characterize the geometrically doubling condition of a metric space in terms of the uniform $L^1$-boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.

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.…

Bayart and Ruzsa [Ergodic Theory Dynam. Systems 35 (2015)] have recently shown that every frequently hypercyclic weighted shift on $\ell^p$ is chaotic. This contrasts with an earlier result of Bayart and Grivaux [Proc. London Math. Soc. (3)…

This article is concerned with the effect of time-periodic forcing on a vector field exhibiting an attracting heteroclinic network. We show that as the forcing frequency tends to infinity, the dynamics reduces to that of a network under…