Results 21 to 30 of about 49 (41)

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., Alfredo Peris, Ajda Fošner   +2 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, Yu-Hsien Chang, Josef Diblík   +2 more
wiley   +1 more source

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, J. Alberto Conejero, Elena Litsyn   +2 more
wiley   +1 more source

On Some Normality‐Like Properties and Bishop′s Property (β) for a Class of Operators on Hilbert Spaces

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, Shigeru Kanemitsu   +1 more
wiley   +1 more source

Notes on subspace-hypercyclic operators

Journal of Mathematical Analysis and Applications, 2013
Let \(X\) be a separable infinite-dimensional Banach space. A recent new notion in linear dynamics was introduced by \textit{B. F. Madore} and \textit{R. A. Martínez-Avendaño} in [J. Math. Anal. Appl. 373, No. 2, 502--511 (2011; Zbl 1210.47023)], namely, the notion of subspace-hypercyclicity.
openaire   +2 more sources

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

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
wiley   +1 more source

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

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, K. Hedayatian, B. Yousefi, John Rassias   +3 more
wiley   +1 more source

Nonwandering operators in Banach space

International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 24, Page 3895-3908, 2005., 2005
We introduce nonwandering operators in infinite‐dimensional separable Banach space. They are new linear chaotic operators and are relative to hypercylic operators, but different from them. Firstly, we show some examples for nonwandering operators in some typical infinite‐dimensional Banach spaces, including Banach sequence space and physical background
Lixin Tian, Jiangbo Zhou, Xun Liu, Guangsheng Zhong   +3 more
wiley   +1 more source