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Linear chaos and frequent hypercyclicity


Author: Quentin Menet
Journal: Trans. Amer. Math. Soc. 369 (2017), 4977-4994
MSC (2010): Primary 47A16; Secondary 37A25, 47A35, 47A75
DOI: https://doi.org/10.1090/tran/6808
Published electronically: February 13, 2017
MathSciNet review: 3632557
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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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Additional Information

Quentin Menet
Affiliation: Département de Mathématique, Université de Mons, 20 Place du Parc, Mons, Belgique
Email: Quentin.Menet@umons.ac.be, quentin.menet@univ-artois.fr

DOI: https://doi.org/10.1090/tran/6808
Keywords: Hypercyclicity, frequent hypercyclicity, linear chaos
Received by editor(s): April 1, 2015
Received by editor(s) in revised form: August 19, 2015
Published electronically: February 13, 2017
Additional Notes: The author was a postdoctoral researcher of the Belgian FNRS
Article copyright: © Copyright 2017 American Mathematical Society

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