In the early 1970's Eisenberg and Hedlund investigated relationships between expansivity
and spectrum of operators on Banach spaces. In this paper we establish relationships …

We answer one of the main current questions in Linear Dynamics by constructing a chaotic
operator which is not $\mathcal {U} $-frequently hypercyclic and thus not frequently …

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 …

We study different pointwise recurrence notions for linear dynamical systems from the
Ergodic Theory point of view. We show that from any reiteratively recurrent vector x 0, for an …

Four notions of distributional chaos, namely DC1, DC2, DC 2 1 2 and DC3, are studied
within the framework of operators on Banach spaces. It is known that, for general dynamical …

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 …

We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We
show that it differs from the notion of distributional chaos of type 2, contrary to what happens …

Linear Dynamical Systems on Hilbert Spaces: Typical Properties and Explicit Examples Page
1 Number 1315 Linear Dynamical Systems on Hilbert Spaces: Typical Properties and Explicit …

A bounded linear operator T acting on a Hilbert space H is said to be recurrent if for every
non-empty open subset U⊂ H there is an integer n such that T n (U)∩ U≠∅. In this paper …

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