Results 31 to 40 of about 100 (68)
The Strong Disjoint Blow‐Up/Collapse Property
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 Let X be a topological vector space, and let ℬ(X) be the algebra of continuous linear operators on X . The operators T1, …, TN ∈ ℬ(X) are disjoint hypercyclic if there is x ∈ X such that the orbit {(T1n(x),…,TNn(x)):n∈ℕ} is dense in X × …×X . Bès and Peris have shown that if T1, …, TN satisfy the Disjoint Blow‐up/Collapse property, then they are ...
Héctor N. Salas, Ajda Fošner
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Subspace-diskcyclic sequences of linear operators [PDF]
Sahand Communications in Mathematical Analysis, 2017 A sequence ${T_n}_{n=1}^{infty}$ of bounded linear operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}
Mohammad Reza Azimi
doaj
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
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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
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Devaney Chaos and Distributional Chaos in the Solution of Certain Partial Differential Equations
Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 The notion of distributional chaos has been recently added to the study of the linear dynamics of operators and C0‐semigroups of operators. We will study this notion of chaos for some examples of C0‐semigroups that are already known to be Devaney chaotic.
Xavier Barrachina +2 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 We prove some further properties of the operator T ∈ [nQN] (n‐power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator T ∈ [nQN] satisfying the translation invariant property is normal and that the operator T ∈ [nQN] is not supercyclic provided that it is not invertible. Also, we study some cases in which an operator T ∈ [
Sid Ahmed Ould Ahmed Mahmoud +1 more
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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
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On a Chaotic Weighted Shift zpdp+1/dzp+1 of Order p in Bargmann Space
Advances in Mathematical Physics, Volume 2011, Issue 1, 2011., 2011 This paper is devoted to the study of the chaotic properties of some specific backward shift unbounded operators Hp=A*pAP+1; p = 0,1,… realized as differential operators in Bargmann space, where A and A* are the standard Bose annihilation and creation operators such that [A, A*] = I.
Abdelkader Intissar, B. G. Konopelchenko
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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
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Supercyclicity and Hypercyclicity of an Isometry Plus a Nilpotent
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 Suppose that X is a separable normed space and the operators A and Q are bounded on X. In this paper, it is shown that if AQ = QA, A is an isometry, and Q is a nilpotent then the operator A + Q is neither supercyclic nor weakly hypercyclic. Moreover, if the underlying space is a Hilbert space and A is a co‐isometric operator, then we give sufficient ...
S. Yarmahmoodi +3 more
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