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$\epsilon$-hypercyclic operators that are not $\delta$-hypercyclic for $\delta$ < $\epsilon$

, 2023
For every fixed $\epsilon$ $\in$ (0, 1), we construct an operator on the separable Hilbert space which is $\delta$-hypercyclic for all $\delta$ $\in$ ($\epsilon$, 1) and which is not $\delta$-hypercyclic for all $\delta$ $\in$ (0, $\epsilon$).
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Disjoint hypercyclic operators [PDF]

Studia Mathematica, 2007
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ON THE HEREDITARILY HYPERCYCLIC OPERATORS

Journal of the Korean Mathematical Society, 2006
Bahman Yousefi, Ali Farrokhinia
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Analytic hypercyclic operators

Matematychni Studii, 2008
Z. H. Mozhyrovska, A. V. Zagorodnyuk
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Syndetically Hypercyclic Operators

Integral Equations and Operator Theory, 2005
A sequence \((T_n)_{n\geq 0}\) of bounded operators on a separable \(\mathcal{F}\)-space \(X\) is hypercyclic if there exists a vector \(x\) in \(X\) such that the set \(\{T_n x \; ; \; n\geq 0\}\) is dense in \(X\). An operator \(T\) on \(X\) is hypercyclic if the sequence \((T^n)_{n\geq 0}\) of its powers is hypercyclic.
Peris, Alfredo, Saldivia, Luis
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Numerically Hypercyclic Operators

Integral Equations and Operator Theory, 2012
Sung Guen Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0009854). A. Peris was supported in part by MICINN and FEDER, Project MTM2010-14909, and by Generalitat Valenciana, Project PROMETEO/2008/101.
Kim, Sung Guen, Song, Hyun Gwi, Peris Manguillot, Alfredo   +2 more
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Multi-hypercyclic operators are hypercyclic

Mathematische Zeitschrift, 2001
An operator \(T\) on a separable complex Hilbert space \(\mathcal H\) space is said to be hypercyclic if there is a vector \(x\) such that the orbit \(\{T^nx: n=0,1,\ldots\}\) is dense in \(\mathcal H\). An operator is said to be supercyclic if there is a vector \(x\) such that the scalar multiples of the elements in the orbit are dense in \(\mathcal H\
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Rotations of Hypercyclic and Supercyclic Operators

Integral Equations and Operator Theory, 2004
A (bounded linear) operator \(T\) on a Banach space \(X\) is called hypercyclic if there is a vector \(x \in X\) such that its orbit \(\{T^n(x) \;| \;n=0,1,2,... \}\) is dense in \(X\); the vector \(x\) is called hypercyclic for \(T\). The operator \(T\) is called supercyclic if \(\{ \alpha T^n(x) \;| \alpha \in \mathbb C, n \in \mathbb N \}\) is dense
León-Saavedra, Fernando, Müller, Vladimír   +1 more
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Faber-hypercyclic operators

Israel Journal of Mathematics, 2008
Let \(X\) be a complex infinite-dimensional separable Banach space and \(T\) be a bounded linear operator on \(X\). Let \(\Omega\) be a bounded domain of the complex plane whose boundary is a closed Jordan curve and \((F_n^{\Omega})_{n\geq 0}\) be the sequence of Faber polynomials of \(\Omega\).
Badea, Catalin, Grivaux, Sophie
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Residuality of Sets of Hypercyclic Operators

Integral Equations and Operator Theory, 2011
Let \(X\) be a separable metrizable topological vector space and let \(L(X)\) denote the set of continuous and linear operators from \(X\) to \(X\). An operator \(T\in L(X)\) is called \textit{hypercyclic} if there exists a vector \(x\in X\) such that \(\{T^n x:n\in\mathbb{N}\}\) is dense in \(X\), and it is said to be \textit{supercyclic} if there ...
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