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2018-09-01 - Article/Dans un journal avec peer-review - Anglais - 38 page(s)

Grosse-Erdmann Karl , "Upper frequent hypercyclicity and related notions" in Revista Matemática Complutense, 31, 3, 673-711

  • Edition : Universidad Complutense de Madrid (Spain)
  • Codes CREF : Mathématiques (DI1100), Systèmes chaotiques (DI1217), Analyse fonctionnelle (DI1122)
  • Unités de recherche UMONS : Probabilité et statistique (S844)
  • Instituts UMONS : Institut de Recherche sur les Systèmes Complexes (Complexys)
  • Centres UMONS : Modélisation mathématique et informatique (CREMMI)
Texte intégral :

Abstract(s) :

(Anglais) Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper frequently hypercyclic weighted backward shifts on sequence spaces, which in turn allows us to come up with various counter-examples in linear dynamics that are substantially simpler than those previously obtained in the literature. More generally, we introduce the notion of upper Furstenberg families A and show that our main results hold for the corresponding A-hypercyclic operators.


Mots-clés :
  • (Anglais) reiteratively hypercyclic operator
  • (Anglais) Furstenberg family
  • (Anglais) Frequently hypercyclic operator
  • (Anglais) Upper frequently hypercyclic operator
  • (Anglais) Upper Furstenberg family
  • (Anglais) Weighted backward shift operator