66 citations · 230 across the 15 of their papers we have counts for
16 papers
The specification property for composition operators
Nilson C. Bernardes, Emma D'Aniello, Martina Maiuriello
It is known that the operator specification property does not coincide, in general, with other notions of chaos in linear dynamics. In this paper, we show that, for a natural and w…
On the Dynamics of Weighted Composition Operators II
Nilson C. Bernardes, Antonio Bonilla, João V. A. Pinto
We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous function…
On Notions of Expansivity for Operators on Locally Convex Spaces
Nilson C. Bernardes, Félix Martínez-Giménez, Francisco Rodenas
We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average exp…
On the Dynamics of Weighted Composition Operators
Nilson C. Bernardes, Antonio Bonilla, João V. A. Pinto
We study the properties of power-boundedness, Li-Yorke chaos, distributional chaos, absolutely Cesàro boundedness and mean Li-Yorke chaos for weighted composition operators on $L^p…
Li-Yorke Chaotic Weighted Composition Operators
Nilson C. Bernardes, Fernanda M. Vasconcellos
We establish complete characterizations of the notion of Li-Yorke chaos for weighted composition operators on spaces and on spaces. As a consequence, we obtain si…
On the Stability of Generalized Hyperbolic Operators
Nilson C. Bernardes
Our main goal is to prove that every invertible generalized hyperbolic operator on a Banach space has a stability property, known as time-dependent stability, which was introduced…
Generalized Hyperbolicity, Stability and Expansivity for Operators on Locally Convex Spaces
Nilson C. Bernardes, Blas M. Caraballo, Udayan B. Darji +2
We introduce and study the notions of (generalized) hyperbolicity, topological stability and (uniform) topological expansivity for operators on locally convex spaces. We prove that…
On Shadowing and Chain Recurrence in Linear Dynamics
Nilson C. Bernardes, Alfredo Peris
In the present work we study the concepts of shadowing and chain recurrence in the setting of linear dynamics. We prove that shadowing and finite shadowing always coincide for oper…
Uniformly Positive Entropy of Induced Transformations
Nilson C. Bernardes, Udayan B. Darji, Rômulo M. Vermersch
Let be a topological dynamical system consisting of a compact metric space and a continuous surjective map . By using local entropy theory, we prove that $…
A generalized Grobman-Hartman theorem
Nilson C. Bernardes, Ali Messaoudi
We prove that any generalized hyperbolic operator on any Banach space is structurally stable. As a consequence, we obtain a generalization of the classical Grobman-Hartman theorem.
Shadowing and structural stability in linear dynamical systems
Nilson C. Bernardes, Ali Messaoudi
A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained…
Li-Yorke Chaos for Composition Operators on -Spaces
N. C. Bernardes, U. B. Darji, B. Pires
Li-Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained re…
Mean Li-Yorke chaos in Banach spaces
N. C. Bernardes, A. Bonilla, A. Peris
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…
Expansivity and Shadowing in Linear Dynamics
Nilson C. Bernardes, Patricia R. Cirilo, Udayan B. Darji +2
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 betwee…
On the Dynamics of Induced Maps on the Space of Probability Measures
Nilson C. Bernardes, Rômulo M. Vermersch
For the generic continuous map and for the generic homeomorphism of the Cantor space, we study the dynamics of the induced map on the space of probability measures, with emphasis o…
Graph Theoretic Structure of Maps of the Cantor Space
Nilson C. Bernardes, Udayan B. Darji
In this paper we develop unifying graph theoretic techniques to study the dynamics and the structure of the space of homeomorphisms and the space of self-maps of the Cantor space.…