66 citations · 175 across the 28 of their papers we have counts for
19 papers · 1 filter
Dynamics on fences
Jernej Činč, Udayan B. Darji, Benjamin Vejnar
Homeomorphisms of the Cantor set play a central role in topology, dynamical systems and descriptive set theory. In parallel, several classes of fence-like spaces - such as the hair…
Dynamics of composition operators induced by odometers
Udayan B. Darji, Daniel Gomes, Régis Varão
We study the linear dynamics of composition operators induced by measurable transformations on finite measure spaces, with particular emphasis on operators induced by odometers. Ou…
Dynamical pair assignments
Udayan B. Darji, Felipe García-Ramos
Relations between points in the phase space are central to the study of topological dynamical systems. Since many of these relations share common properties, it is natural to study…
Shadowing in the hyperspace of continua
Bernardo Carvalho, Udayan Darji
We discuss whether classical examples of dynamical systems satisfying the shadowing property also satisfy the shadowing property for the induced map on the hyperspace of continua,…
Shift operators and their classification
Maria Carvalho, Udayan B. Darji, Paulo Varandas
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 weighte…
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…
Shift-like Operators on
Emma D'Aniello, Udayan B. Darji, Martina Maiuriello
In this article we develop a general technique which takes a known characterization of a property for weighted backward shifts and lifts it up to a characterization of that propert…
Local entropy theory and descriptive complexity
Udayan B. Darji, Felipe García-Ramos
We investigate local entropy theory, particularly the property of having completely positive entropy (CPE), from a descriptive set-theoretic point of view. We aim to determine desc…
Generalized Hyperbolicity and Shadowing in spaces
Emma D'Aniello, Udayan B. Darji, Martina Maiuriello
It is rather well-known that hyperbolic operators have the shadowing property. In the setting of finite dimensional Banach spaces, having the shadowing property is equivalent to be…
Chaos and frequent hypercyclicity for composition operators
Udayan B. Darji, Benito Pires
The notions of chaos and frequent hypercyclicity enjoy an intimate relationship in linear dynamics. Indeed, after a series of partial results, it was shown by Bayart and Rusza in 2…
Shadowing, Finite Order Shifts and Ultrametric Spaces
Udayan B. Darji, Daniel Gonçalves, Marcelo Sobottka
Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, and ultrametric complete spaces. We develop a the…
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 $…
Linear Dynamics Induced by Odometers
Donatella Bongiorno, Emma D'Aniello, Udayan B. Darji +1
Weighted shifts are an important concrete class of operators in linear dynamics. In particular, they are an essential tool in distinguishing variety dynamical properties. Recently,…
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…
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…
Topological transivity and mixing of the composition operators
Udayan B. Darji, Benito Pires
Let be a -finite measure space and \mbox{} be a measurable transformation such that the composition operator is a bounded…
Some universality results for dynamical systems
Udayan B. Darji, Étienne Matheron
We prove some "universality" results for topological dynamical systems. In particular, we show that for any continuous self-map of a perfect Polish space, one can find a dense,…
Chaos and Indecomposability
Udayan B. Darji, Hisao Kato
We use recent developments in local entropy theory to prove that chaos in dynamical systems implies the existence of complicated structure in the underlying space. Earlier Mouron p…
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.…