Results 41 to 50 of about 142 (132)

Plank theorems and their applications: A survey

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
wiley   +1 more source

Epsilon-hypercyclic operators [PDF]

Ergodic Theory and Dynamical Systems, 2009
AbstractLet X be a separable infinite-dimensional Banach space, and T a bounded linear operator on X; T is hypercyclic if there is a vector x in X with dense orbit under the action of T. For a fixed ε∈(0,1), we say that T is ε-hypercyclic if there exists a vector x in X such that for every non-zero vector y∈X there exists an integer n with $\|T^nx-y ...
Badea, Catalin, Grivaux, Sophie, Müller, Vladimir   +2 more
openaire   +2 more sources

δ‐Almost Periodic Vectors for Bounded Linear Operators: Geometric and Dynamical Structure

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
We introduce δ‐almost periodic vectors for bounded linear operators on Banach spaces, defined by uniform recurrence to the base point within a fixed tolerance δ ≥ 0. This yields a quantitative relaxation of the case δ = 0. We develop basic structural properties of the classes APδ(T), including monotonicity in δ, positive homogeneity, forward invariance
Hadi Obaid Alshammari, Otmane Benchiheb, Marko Kostic   +2 more
wiley   +1 more source

Powers of Convex‐Cyclic Operators

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
A bounded operator T on a Banach space X is convex cyclic if there exists a vector x such that the convex hull generated by the orbit Tnxn≥0 is dense in X. In this note we study some questions concerned with convex‐cyclic operators. We provide an example of a convex‐cyclic operator T such that the power Tn fails to be convex cyclic.
Fernando León-Saavedra, María del Pilar Romero-de la Rosa, Manuel Maestre   +2 more
wiley   +1 more source

Sums of hypercyclic operators

Journal of Functional Analysis, 2003
A (bounded) operator \(T\) on a complex infinite-dimensional separable Banach space \(X\) is said to be hypercyclic if there is a (hypercyclic) vector \(x \in X\) such that its orbit \(O(T,x):=\{x,Tx,T^2x,\dots\}\) is dense in \(X\). The operator \(T\) is called chaotic if it is hypercyclic and the set of periodic points of \(T\) is dense in \(X ...
openaire   +2 more sources

Interactions between universal composition operators and complex dynamics

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract This paper is concerned with universality properties of composition operators Cf$C_f$, where the symbol f$f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of Cf$C_f$ when f$f$ is restricted to (subsets of) Baker and wandering domains.
Vasiliki Evdoridou, Clifford Gilmore, Myrto Manolaki   +2 more
wiley   +1 more source

Generalized bilateral shifts of higher multiplicity [PDF]

Arab Journal of Mathematical Sciences
PurposeSince weighted shifts play a vital role in linear dynamics so in 2021 Chan & Sanders considered weighted shift operators on ℓp(Z) that are not hypercyclic and proved that under certain conditions they can be factorized as products of hypercyclic ...
Munmun Hazarika, Silpi Sikha Das
doaj   +1 more source

Advanced Extensions and Applications of Transitivity and Mixing in Set‐Valued Dynamics With Numerical Simulations and Visual Insights

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This article extends Alfredo Peris’s work on chaos in set‐valued dynamics by providing new characterizations and applications of transitivity and mixing properties. Peris demonstrated that the topological transitivity of a set‐valued map is closely related to the weak mixing property of the individual map.
Illych Alvarez, Mehmet Ünver
wiley   +1 more source

On subspace-diskcyclicity

Arab Journal of Mathematical Sciences, 2017
In this paper, we define and study subspace-diskcyclic operators. We show that subspace-diskcyclicity does not imply diskcyclicity. We establish a subspace-diskcyclic criterion and use it to find a subspace-diskcyclic operator that is not subspace ...
Nareen Bamerni, Adem Kılıçman
doaj   +1 more source

Chaos on Fuzzy Dynamical Systems

Mathematics, 2021
Given a continuous map f:X→X on a metric space, it induces the maps f¯:K(X)→K(X), on the hyperspace of nonempty compact subspaces of X, and f^:F(X)→F(X), on the space of normal fuzzy sets, consisting of the upper semicontinuous functions u:X→[0,1] with ...
Félix Martínez-Giménez, Alfred Peris, Francisco Rodenas   +2 more
doaj   +1 more source