Hypercyclic operators and related topics

Hypercyclicity, strictly speaking, dates back to 1929 when the first example in the literature appeared. However it was not until the mid-80's, with the discovery of the Hypercyclicity Criterion, that this theory started its evolution. This criterion embraces the conditions that assure a continuous linear operator to be hypercyclic. A considerable number of hypercyclic operators satisfy these conditions. Indeed, every single example known until 2007 satisfied such criterion. It was natural to posed the question if all the hypercyclicity operators must satisfy the Hypercyclicity Criterion, such a question is known as the Great Open Problem in the theory of hypercyclicity.EThOS - Electronic Theses Online ServiceGBUnited Kingdo