Operator on the space of rapidly decreasing functions with all non-zero vectors hypercyclic

Small sets and hypercyclic vectors

We study the “smallness” of the set of non-hypercyclic vectors for some classical hypercyclic operators.

on the effect of linear & non-linear texts on students comprehension and recalling

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Common Hypercyclic Vectors for Families of Operators

We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators, which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy space, generalizing recent results by...

Each Non - Zero Convolution Operator on the Entire Functions Admits a Continuous Linear Right Inverse

Common Hypercyclic Vectors for Composition Operators

A continuous operator acting on a topological vector space X is called hypercyclic provided there exists a vector x ∈ X such that its orbit {T nx; n ≥ 1} is dense in X. Such a vector is called a hypercyclic vector for T . The set of hypercyclic vectors will be denoted by HC(T ). The first example of hypercyclic operator was given by Birkhoff, 1929 [3], who shows that the operator of translation...