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$q$-Frequently hypercyclic operators [PDF]
Banach Journal of Mathematical Analysis, 2015 13 pages, to ...
Gupta, Manjul, Mundayadan, Aneesh
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Hypercyclic operators are subspace hypercyclic
Journal of Mathematical Analysis and Applications, 2016 A bounded operator \(T\) on a separable Banach space \(X\) is called subspace hypercyclic for a subspace \(M\) of \(X\) if there is a vector \(x \in X\) such that the intersection of its orbit and \(M\) is dense in \(M\). The aim of this paper is to solve a question of \textit{B. F. Madore} and \textit{R. A. Martínez-Avendaño} [J. Math. Anal. Appl. 373,
Nareen Bamerni +2 more
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On the Non-Hypercyclicity of Normal Operators, Their Exponentials, and Symmetric Operators
Mathematics, 2019 We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator A in a complex Hilbert space as well as of the collection e t A t ≥ 0 of its exponentials, which, under a certain ...
Marat V. Markin, Edward S. Sichel
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Linear dynamics of semigroups generated by differential operators
Open Mathematics, 2017 During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the sense of Li-Yorke, subchaos, mixing ...
Alberto Conejero J. +3 more
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CHAOTIC AND HYPERCYCLIC OPERATORS ON SOLID BANACH FUNCTION SPACES
Проблемы анализа, 2020 In this paper, we study hypercyclicity on solid Banach function spaces, and give the characterization for weighted translation operators to be hypercyclic in terms of weight and aperiodic functions.
C-C. Chen, S. M. Tabatabaie
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Topologically mixing extensions of endomorphisms on Polish groups
Applied General Topology, 2022 In this paper we study the dynamics of continuous endomorphisms on Polish groups. We offer necessary and sufficient conditions for a continuous endomorphism on a Polish group to be weakly mixing.
John Burke, Leonardo Pinheiro
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Countably Generated Algebras of Analytic Functions on Banach Spaces
Axioms, 2023 In the paper, we study various countably generated algebras of entire analytic functions on complex Banach spaces and their homomorphisms. Countably generated algebras often appear as algebras of symmetric analytic functions on Banach spaces with respect
Zoriana Novosad +2 more
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Analytic Automorphisms and Transitivity of Analytic Mappings
Mathematics, 2020 In this paper, we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators.
Zoriana Novosad, Andriy Zagorodnyuk
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Hypercyclic weighted shifts [PDF]
Transactions of the American Mathematical Society, 1995 Summary: An operator \(T\) acting on a Hilbert space is hypercyclic if, for some vector \(x\) in the space, the orbit \(\{T^ n x: n\geq 0\}\) is dense. In this paper we characterize hypercyclic weighted shifts in terms of their weight sequences and identify the direct sums of hypercyclic weighted shifts which are also hypercyclic.
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Journal d'Analyse Mathématique, 2020 We completely characterize the finite dimensional subsets A of any separable Hilbert space for which the notion of A-hypercyclicity coincides with the notion of hypercyclicity, where an operator T on a topological vector space X is said to be A-hypercyclic if the set {T n x, n $\ge$ 0, x $\in$ A} is dense in X.
Charpentier, Stéphane, Ernst, Romuald
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