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Quentin MENET
University of Mons (France)
Linear chaos and frequent hypercyclicity
February 13, 2015 1pm, 646 PGH
Abstract
Let T be a continuous and linear operator on a Banach space X. We say
that T is hypercyclic if there is some vector whose the orbit visits (infinitely
often) each non-empty open subset of X. During the last decade, the researchers in
linear dynamics have investigated the frequency of these visits and several
variants of the notion of hypercyclicity have been introduced: the frequent
hypercyclicity, the U-frequent hypercyclicity and the reiterative hypercyclicity.
The goal of this talk is to investigate the links between these different notions
of hypercyclicity and their link with linear chaos. In particular, we answer one of
the main current questions in linear dynamics by showing that there exists a
chaotic operator which is not frequently hypercyclic.
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Last modified: April 08 2016 - 07:21:37