Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2019

A quantitative interpretation of the frequent hypercyclicity criterion

Résumé

We give a quantitative interpretation of the frequent hypercyclicity criterion. Actually we show that an operator which satisfies the frequent hypercyclicity criterion is necessarily $A$ -frequently hypercyclic, where $A$ refers to some weighted densities sharper than the natural lower density. In that order, we exhibit different scales of weighted densities that are of interest to quantify the ‘frequency’ measured by the frequent hypercyclicity criterion. Moreover, we construct an example of a unilateral weighted shift which is frequently hypercyclic but not $A$ -frequently hypercyclic on a particular scale.

Dates et versions

hal-04357466 , version 1 (21-12-2023)

Identifiants

Citer

Romuald Ernst, Augustin Mouze. A quantitative interpretation of the frequent hypercyclicity criterion. Ergodic Theory and Dynamical Systems, 2019, 39 (4), pp.898-924. ⟨10.1017/etds.2017.55⟩. ⟨hal-04357466⟩
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