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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Frequently hypercyclic operators
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by Frédéric Bayart and Sophie Grivaux PDF
Trans. Amer. Math. Soc. 358 (2006), 5083-5117 Request permission


We investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators $T$ on separable complex $\mathcal {F}$-spaces: $T$ is frequently hypercyclic if there exists a vector $x$ such that for every nonempty open subset $U$ of $X$, the set of integers $n$ such that $T^{n}x$ belongs to $U$ has positive lower density. We give several criteria for frequent hypercyclicity, and this leads us in particular to study linear transformations from the point of view of ergodic theory. Several other topics which are classical in hypercyclicity theory are also investigated in the frequent hypercyclicity setting.
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Additional Information
  • Frédéric Bayart
  • Affiliation: Laboratoire Bordelais d’Analyse et de Géométrie, UMR 5467, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France
  • MR Author ID: 683115
  • Email:
  • Sophie Grivaux
  • Affiliation: Laboratoire Paul Painlevé, UMR 8524, Université des Sciences et Technologies de Lille, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France
  • MR Author ID: 705957
  • Email:
  • Received by editor(s): April 15, 2004
  • Received by editor(s) in revised form: November 25, 2004
  • Published electronically: June 20, 2006
  • Additional Notes: This work was supported in part by the European Community’s Human Potential Programme under contract HPRN-CT-2000-00116 (Analysis and Operators)
  • © Copyright 2006 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 5083-5117
  • MSC (2000): Primary 47A16, 47A35, 37B05, 37A05
  • DOI:
  • MathSciNet review: 2231886