Results 61 to 70 of about 752 (101)
Common hypercyclic vectors for families of backward shift operators [PDF]
Journal of Operator Theory, 2017 We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the full orbit of the backward shift.
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Discrete cyclic systems and circle congruences. [PDF]
Ann Mat Pura Appl, 2022 Hertrich-Jeromin U, Szewieczek G.
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Invariant manifolds of hypercyclic vectors for the real scalar case [PDF]
Proceedings of the American Mathematical Society, 1999 We show that every hypercyclic operator on a real locally convex vector space admits a dense invariant linear manifold of hypercyclic vectors.
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The Specification Property for $C_0$-Semigroups
, 2018 We study one of the strongest versions of chaos for continuous dynamical systems, namely the specification property. We extend the definition of specification property for operators on a Banach space to strongly continuous one-parameter semigroups of ...
Bartoll, S. +3 more
core
Luh hypercyclic vector for composition operator
In this paper, we deal with the construction of holomorphic functions on a simply connected domain satisfying that all its derivatives and antiderivatives under a composition operator have a dense orbit. Such functions will be called Luh hypercyclic vectors for the respective composition operator.
Benchiheb, Otmane +3 more
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An operator on a separable Hilbert space with many hypercyclic vectors [PDF]
Studia Mathematica, 1987 Let T be a linear continuous operator acting in a Hilbert space H. A point \(x_ 0\in H\) is said to be cyclic if \(H=span(x_ 0,Tx_ 0,T\) \(2x_ 0,...)\) and hypercyclic if the orbit \((x_ 0,Tx_ 0,T\) \(2x_ 0,...)\) is dense in H. There is given a construction of a separable Hilbert space H (over complexes) and an operator T with a cyclic vector \(x_ 0\)
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Hypercyclic and supercyclic linear operators on non-Archimedean vector spaces
, 2017 A main objective of the present paper is to develop the theory of hypercyclicity and supercyclicity of linear operators on topological vector space over non-Archimedean valued fields. We show that there does not exist any hypercyclic operator on finite dimensional spaces.
Mukhamedov, Farrukh, Khakimov, Otabek
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Existence of common hypercyclic vectors for translation operators
, 2014 We prove the existence of common hypercyclic, entire functions for certain families of translation operators.
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On the complexity of upper frequently hypercyclic vectors
Given a continuous linear operator $T:X\to X$, where $X$ is a topological vector space, let $\mathrm{UFHC}(T)$ be the set of upper frequently hypercyclic vectors, that is, the set of vectors $x \in X$ such that $\{n \in ω: T^nx \in U\}$ has positive upper asymptotic density for all nonempty open sets $U\subseteq X$.
Glab, Szymon, Leonetti, Paolo
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