We investigate the subject of linear dynamics by studying the notion of frequent
hypercyclicity for bounded operators $ T $ on separable complex $\mathcal {F} $-spaces …

We generalize the notions of hypercyclic operators, U U-frequently hypercyclic operators
and frequently hypercyclic operators by introducing a new concept in linear dynamics …

We show that under no hypotheses on the density of the ranges of the mappings involved,
an almost-commuting sequence (Tn) of operators on an F-space X satisfies the …

We show that a continuous linear operator T on a Fréchet space satisfies the so-called
Hypercyclicity Criterion if and only if it is hereditarily hypercyclic, and if and only if the direct …

A bounded linear operator $ T $ on a Banach space $ X $ is called frequently hypercyclic if
there exists $ x\in X $ such that the lower density of the set $\{n\in\mathbb {N}: T^ nx\in U\} …

We study frequently hypercyclic operators, a natural new concept in hypercyclicity that was
recently introduced by F. Bayart and S. Grivaux. We derive a strengthened version of their …

Let $ X $ be a separable Fréchet space. We prove that a linear operator $ T: X\to X $
satisfying a special case of the Hypercyclicity Criterion is topologically mixing, ie for any …

In these notes we report on recent progress in the theory of hypercyclic and chaotic
operators. Our discussion will be guided by the following fundamental problems: How to …

Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear
dynamics, we study various stronger forms of recurrence for linear operators, in particular …

An operator (linear and continuous) in a Fréchet space is hypercyclic if there exists a vector
whose orbit under the operator is dense. If the scalar multiples of the elements in the orbit …