Results 11 to 20 of about 106 (90)
Fast orbital convergence reveals more hypercyclic vectors
Applied General TopologyLet X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a ...
T. K. Subrahmonian Moothathu
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Invariant Manifolds of Hypercyclic Vectors [PDF]
Proceedings of the American Mathematical Society, 1993 We show that any hypercyclic operator on Hilbert space has a dense, invariant linear manifold consisting, except for zero, entirely of hypercyclic vectors.
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Linear Structure of Hypercyclic Vectors
Journal of Functional Analysis, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
León-Saavedra, Fernando +1 more
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Hypercyclic operators on topological vector spaces [PDF]
Journal of the London Mathematical Society, 2012 The paper is submitted to Journal of ...
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Algebrable sets of hypercyclic vectors for convolution operators [PDF]
Israel Journal of Mathematics, 2020 We show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff's operator also has this property on the space of complex-valued smooth functions on the real line.
Bès, Juan, Papathanasiou, Dimitris
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Frequently hypercyclic random vectors
Proceedings of the American Mathematical Society, 2022 We show that, under suitable conditions, an operator acting like a shift on some sequence space has a frequently hypercyclic random vector whose distribution is strongly mixing for the operator. This result will be applied to chaotic weighted shifts.
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Common hypercyclic vectors and dimension of the parameter set
Indiana University Mathematics Journal, 2022 We investigate the existence of a common hypercyclic vector for a family $(T_λ)_{λ\in Λ}$ of hypercyclicoperators acting on the same Banach space $X$. We give positive and negative results involving the dimension of $Λ$ and the regularity of each map $λ\in Λ\mapsto T_λ^n x$, $x\in X$, $n\in\mathbb N$.
Bayart, Frédéric +2 more
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Chaos for Cosine Operator Functions on Groups
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Let 1 ≤ p < ∞ and G be a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue space Lp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously.
Chung-Chuan Chen, Wei-Shih Du
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Powers of Convex‐Cyclic Operators
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 A bounded operator T on a Banach space X is convex cyclic if there exists a vector x such that the convex hull generated by the orbit Tnxn≥0 is dense in X. In this note we study some questions concerned with convex‐cyclic operators. We provide an example of a convex‐cyclic operator T such that the power Tn fails to be convex cyclic.
Fernando León-Saavedra +2 more
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Banach spaces of hypercyclic vectors.
Michigan Mathematical Journal, 1996 Dirección General de Investigación Científica y ...
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