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Frequent universality criterion and densities

Part of:Topological dynamicsGeneral theory of linear operators

Published online by Cambridge University Press:  25 November 2019

R. ERNST and
A. MOUZE
R. ERNST
Affiliation:
Romuald Ernst, LMPA, Centre Universitaire de la Mi-Voix, Maison de la Recherche Blaise-Pascal, 50 rue Ferdinand Buisson, BP 699, 62228 Calais Cedex, France email ernst.r@math.cnrs.fr
A. MOUZE
Affiliation:
Augustin Mouze, Laboratoire Paul Painlevé, UMR 8524, Cité Scientifique, 59650 Villeneuve d’Ascq, France email Augustin.Mouze@math.univ-lille1.fr
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Abstract

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We improve a recent result by giving the optimal conclusion both to the frequent universality criterion and the frequent hypercyclicity criterion using the notion of $A$ -densities, where $A$ refers to some weighted densities sharper than the natural lower density. Moreover, we construct an operator which is logarithmically frequently hypercyclic but not frequently hypercyclic.

Keywords

frequent universalityweighted densitieshypercyclicity

MSC classification

Primary:47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary:37B50: Multi-dimensional shifts of finite type, tiling dynamics

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 3 , March 2021, pp. 846 - 868
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Copyright
© Cambridge University Press, 2019

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