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arXiv · 1410.7173

Linear chaos and frequent hypercyclicity

Quentin Menet
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Abstract

We answer one of the main current questions in Linear Dynamics by constructing a chaotic operator on $\ell^1$ which is not $\mathcal{U}$-frequently hypercyclic and thus not frequently hypercyclic. This operator also gives us an example of a chaotic operator which is not distributionally chaotic. We complement this result by showing that every chaotic operator is reiteratively hypercyclic.

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Quentin Menet. 2014-10-27. Linear chaos and frequent hypercyclicity. https://arxiv.org/abs/1410.7173

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