Frequently hypercyclic operators and vectors

By Antonio Bonilla, K. Grosse-Erdmann. Ergodic Theory and Dynamical Systems, 2007

130 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/8b3dd9661a2f296e924f72dd283b5ed37438a22a

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Szemeredi's theorem, frequent hypercyclicity and multiple recurrence (2010, background): “Using the frequent universality criterion from [11] and [12] it is not difficult to show that (λnB)n∈N is frequently universal, where B is the unweighted unilateral backward shift.”
Recurrence properties of hypercyclic operators (2014, methodology): “For hypercyclic operators and frequently hypercyclic operators, we have at our disposal the well-known Hypercyclicity Criterion [9] and the Frequent Hypercyclicity Criterion [10,11].”
A new class of frequently hypercyclic operators (2010, background): “Nonetheless, quite a large number of hypercyclic operators are frequently hypercyclic, at least on Hilbert spaces (see for instance [3], [10]).”
Linear chaos and frequent hypercyclicity (2014, background): “4] and can be found in many papers [8, 11, 17, 20, 23, 25].”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “In fact, the more popular operators (derivative operators, weighted backward shifts, composition operators) satisfy that their respective sets of frequent hypercyclic vectors are not residual; see [47] and [104].”
Linear dynamical systems on Hilbert spaces: typical properties and explicit examples (2017, background): “Frequent hypercyclicity was introduced in [5] and rather extensively studied since then (for instance in [10], [14], [28], [30], [40], [49] .”
Difference sets and frequently hypercyclic weighted shifts (2013, methodology): “This follows from a standard application of the frequent hypercyclicity criterion of [8], which we recall for convenience: Theorem 10.”
Distributional chaos for linear operators (2013, background): “In [8] it was observed that the Frequent Hypercyclicity Criterion implies that T is frequently hypercyclic, Devaney chaotic and mixing.”