Related papers: Common hypercyclic vectors for families of backwar…

Considering a family of upper frequently hypercyclic operators we care about the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for a family of operators to…

We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a…

In this paper, we generalize to the context of algebras some recent results on the existence of common hypercyclic vectors for families of products of backward shift operators. We also give, in a multi-dimensional setting, a positive answer…

We prove the existence of common hypercyclic, entire functions for certain families of translation operators.

We prove that the space $l^2$ contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift operator by constants of absolute value greater than 1.

We study the existence of a common hypercyclic vector for different families of composition operators.

We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences. There exist frequently hypercyclic operators with upper-frequently hypercyclic…

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

We provide with criteria for a family of sequences of operators to share a frequently universal vector. These criteria are variants of the classical Frequent Hypercyclicity Criterion and of a recent criterion due to Grivaux, Matheron and…

We show that, under suitable conditions, an operator acting like a shift on some sequence space has a frequently hypercyclic random vector whose distribution is strongly mixing for the operator. This result will be applied to chaotic…

We prove the existence of algebras of hypercyclic vectors in three cases: convolution operators, composition operators, and backward shift operators.

We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Fr\'echet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case we obtain…

We investigate the existence of a common hypercyclic vector for a family $(T_\lambda)_{\lambda\in \Lambda}$ of hypercyclicoperators acting on the same Banach space $X$. We give positive and negative results involving the dimension of…

We prove the existence of common hypercyclic entire functions for uncountable families of translation type operators. Contrary to our previous work [34], here the parameter which reflects the uncountable family lies on the unit circle. On…

Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper…

We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator $T$ on a complex Fr\'echet space $X$ and a set $\Lambda\subseteq \R_+\times\C$…

We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We…

Let $(T\_\lambda)\_{\lambda\in\Lambda}$ be a family of operators acting on a $F$-space $X$, where the parameter space $\Lambda$ is a subset of $\mathbb R^d$. We give sufficient conditions on the family to yield the existence of a vector…

We show that the non-zero multiples of the derivative operator and the non-zero multiples of non-trivial translation operators on the space of entire functions share a common hypercyclic subspace, i.e. a closed infinite-dimensional subspace…

We study frequently recurrent unilateral and bilateral backward shift operators on Fr\'echet sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent vector, then it supports a dense set of such vectors, so…