Dynamical Systems
Frequently dense orbits
Comptes Rendus. Mathématique, Volume 341 (2005) no. 2, pp. 123-128.

We study the notion of frequent hypercyclicity that was recently introduced by Bayart and Grivaux. We show that frequently hypercyclic operators satisfy the Hypercyclicity Criterion, answering a question of Bayart and Grivaux [Trans. Amer. Math. Soc., in press]. We also disprove a conjecture therein concerning frequently hypercyclic weighted shifts, and we prove that vectors which have a somewhere frequently dense orbit are frequently hypercyclic.

On étudie la notion d'hypercyclicité fréquente qui a récemment été introduite par Bayart et Grivaux. Nous démontrons que tout opérateur fréquemment hypercyclique vérifie le Critère d'Hypercyclicité, ce qui répond à une question de Bayart et Grivaux [Trans. Amer. Math. Soc., à paraître]. De plus, nous réfutons une conjecture de Bayart et Grivaux concernant les shifts à poids fréquemment hypercycliques, et nous démontrons que tout vecteur avec une orbite qui est quelque part fréquemment dense est fréquemment hypercyclique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.05.025
Grosse-Erdmann, K.-G. 1; Peris, Alfredo 2

1 Fachbereich Mathematik, FernUniversität Hagen, 58084 Hagen, Germany
2 E.T.S. Arquitectura, Departament de Matemàtica Aplicada and IMPA-UPV, Universitat Politècnica de València, 46022 València, Spain
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Grosse-Erdmann, K.-G.; Peris, Alfredo. Frequently dense orbits. Comptes Rendus. Mathématique, Volume 341 (2005) no. 2, pp. 123-128. doi : 10.1016/j.crma.2005.05.025. http://archive.numdam.org/articles/10.1016/j.crma.2005.05.025/

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