Linear chaos and frequent hypercyclicity

Menet, Quentin

doi:10.1090/tran/6808

Linear chaos and frequent hypercyclicity
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Trans. Amer. Math. Soc. 369 (2017), 4977-4994 Request permission

Abstract:

We answer one of the main current questions in Linear Dynamics by constructing a chaotic operator 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 and an example of a chaotic operator with only countably many unimodular eigenvalues. We complement this result by showing that every chaotic operator is reiteratively hypercyclic.

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