Results 51 to 60 of about 752 (101)
Dynamics, Operator Theory, and Infinite Holomorphy
, 2014 Abstract and Applied Analysis, Volume 2014, Issue 1, 2014.
Alfred Peris +3 more
wiley +1 more source
Common hypercyclic vectors and universal functions
, 2015 Let X,Y be two separable Banach or Frechet spaces , and (Tn) , n=1,2,... be a sequence from linear and continuous operators from X to Y . We say that the sequence (Tn) , n=1,2,... is universal , if there exists some vector v in X such that the sequence Tn(v) , n=1,2,... is dense in Y . If X=Y we say that the sequence (Tn) is hypercyclic .More generally
Costakis, George, Tsirivas, Nikos
openaire +2 more sources
A new class of frequently hypercyclic operators [PDF]
, 2010 We study a hypercyclicity property of linear dynamical systems: a bounded linear operator T acting on a separable infinite-dimensional Banach space X is said to be hypercyclic if there exists a vector x in X such that {T^{n}x : n>0} is dense in X, and ...
Grivaux, Sophie
core
Common hypercyclic functions for multiples of convolution and non-convolution operators [PDF]
, 2009 We prove the existence of a residual set of entire functions, all of whose members are hypercyclic for every nonzero scalar multiple of T, where T is the differential operator associated to an entire function of order less than 1/2. The same result holds
Bernal González, Luis
core
Existence of Hypercyclic Operators on Topological Vector Spaces
Journal of Functional Analysis, 1997 The author establishes the following result: Suppose \(X\) is a topological vector space with a bounded biorthogonal system \(\{x_n, f_n\}\). Suppose \(X\) is \(\ell^1\)-complete with respect to \((x_n)\). (a) If \(\widetilde T: X\to X\) is continuous and \(\widetilde T(x_n)= w_nx_{n-1}\) for some bounded sequence \((w_n)\) of positive real numbers ...
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On chaotic 𝐶₀-semigroups and infinitely regular hypercyclic vectors [PDF]
Proceedings of the American Mathematical Society, 2006 A C 0 C_0 -semigroup T = ( T ( t ) ) t ≥ 0 \mathcal {T}=(T(t))_{t\geq 0} on a Banach space X X is called hypercyclic if there exists an element
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A hypercyclicity criterion for non-metrizable topological vector spaces [PDF]
Functiones et Approximatio Commentarii Mathematici, 2018 We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition operator on the space of real analytic functions on $]0,1[$, which solves two problems of Bonet and Domański \cite ...
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Mean Li-Yorke chaos in Banach spaces
, 2018 We investigate the notion of mean Li-Yorke chaos for operators on Banach spaces. We show that it differs from the notion of distributional chaos of type 2, contrary to what happens in the context of topological dynamics on compact metric spaces. We prove
Bernardes Jr., N. C. +2 more
core
Hypercyclic vectors and algebras
, 2021 Ce travail contribue à la théorie de l'hypercyclicité et à des concepts liés. Nous nous sommes principalement intéressés à des algèbres de vecteurs hypercycliques pour opérateurs agissant sur une algèbre de Fréchet de suites, bien que quelques contributions portent sur l'existence d'un seul vecteur.
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Common hypercyclic vectors for certain families of differential operators [PDF]
Illinois Journal of Mathematics, 2016 Let (k(n)) n=1,2,... be a strictly increasing sequence of positive integers . We consider a specific sequence of differential operators Tk(n), , n=1,2,... on the space of entire functions , that depend on the sequence (k(n)) n=1,2,... and the non-zero complex number .
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