Results 31 to 40 of about 108 (97)
Common hypercyclic vectors for multiples of backward shift
Journal of Functional Analysis, 2003 We prove that the space $l^2$ contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift operator by constants of absolute value greater than 1.
Abakumov, Evgeny, Gordon, J
openaire +4 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 +2 more
wiley +1 more source
On the set of hypercyclic vectors for the differentiation operator [PDF]
Israel Journal of Mathematics, 2010 Let $D$ be the differentiation operator $Df=f'$ acting on the Fréchet space $\H$ of all entire functions in one variable with the standard (compact-open) topology. It is known since 1950's that the set $H(D)$ of hypercyclic vectors for the operator $D$ is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the
openaire +3 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 +2 more
wiley +1 more source
On the Existence of Polynomials with Chaotic Behaviour
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 We establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) infinite‐dimensional separable Frèchet space admits mixing (hence hypercyclic) polynomials of arbitrary positive degree.
Nilson C. Bernardes Jr. +2 more
wiley +1 more source
On Some Subspace Codiskcyclic Operators in Banach Spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.This paper introduces the concepts of subspace codiskcyclicity and subspace codisk transitivity, providing criteria and examples that highlight their distinct properties compared to traditional codiskcyclic operators and hypercyclic operators. The paper also demonstrates the existence of subspace codiskcyclic operators in finite‐dimensional Banach ...
Peter Masong Slaa +3 more
wiley +1 more source
Frequently Hypercyclic and Chaotic Behavior of Some First‐Order Partial Differential Equation
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We study a particular first‐order partial differential equation which arisen from a biologic model. We found that the solution semigroup of this partial differential equation is a frequently hypercyclic semigroup. Furthermore, we show that it satisfies the frequently hypercyclic criterion, and hence the solution semigroup is also a chaotic semigroup.
Cheng-Hung Hung +2 more
wiley +1 more source
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
Abstract and Applied Analysis, Volume 2024, Issue 1, 2024.In this paper, under appropriate hypotheses, we have the existence of a solution semigroup of partial differential equations with delay operator. These equations are used to describe time–age‐structured cell cycle model. We also prove that the solution semigroup is a frequently hypercyclic semigroup.
Cheng-Hung Hung, Victor Kovtunenko
wiley +1 more source
On the Weakly Hypercyclic Composition Operators on Hardy Spaces
Journal of Mathematical Extension, 2010 An operator T on a Banach space X is said to be weakly hypercyclic if there exists a vector x ∈ X whose orbit under T is weakly dense in X. We show that every weakly hypercyclic composition operator on classic Hardy space H2 is norm hypercyclic.
H. Rezaei
doaj