Hypercyclicity is the study of linear and continuous operators that possess a dense orbit.
Given a separable, infinite dimensional topological vector space X, we say a continuous …

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 linear operator can have an orbit that comes within a bounded distance of
every point, yet is not dense. We also prove that such an operator must be hypercyclic. This …

Let $ A $ be an invertible (bounded linear) operator acting on a complex Banach space
$\mathcal {X} $. $ A $ is called hypercyclic if there is a vector $ y $ in $\mathcal {X} $ such …

An operator T: X→ X is said to be hypercyclic if there exists a vector x∈ X, called hypercyclic
for T, such that the orbit Orb (T, x)={T ⁿx: n∈ ℕ} is dense in X. T is hereditarily hypercyclic if …

If X is a topological vector space and T: X→ X is a continuous linear operator, then T is said
to be hypercyclic when there is a vector x in X such that the set {T nx: n∈ N} is dense in X. If …

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 …

A vector $ x $ in a Hilbert space $\mathcal {H} $ is called hypercyclic for a bounded operator
$ T:\mathcal {H}\rightarrow\mathcal {H} $ if the orbit $\{T^{n} x: n\geq 1\} $ is dense in …

We study in this paper a hypercyclicity property of linear dynamical systems: a bounded
linear operator T acting on a separable infinite-dimensional Banach space X is said to be …

A continuous linear operator $ T: X\to X $ is hypercyclic if there is an $ x\in X $ such that the
orbit $\{T^ nx\} _ {n\geq 0} $ is dense. A result of H. Salas shows that any infinite …