DI-UMONS : Dépôt institutionnel de l’université de Mons

Recherche transversale
Rechercher
(titres de publication, de périodique et noms de colloque inclus)
2017-10-11 - Colloque/Présentation - communication orale - Anglais - 0 page(s)

Mestiri Monia , "Common upper frequent hypercyclicity" in Journées du GDR AFHP, Bordeaux, France, 2017

  • Codes CREF : 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)

Abstract(s) :

(Anglais) An operator on a Banach space is called hypercyclic if it possesses a dense orbit; it is called upper-frequently hypercyclic if it possesses an orbit that is not only dense but that meets every non-empty open set 'very often'. A fundamental theorem in linear dynamics is the transitivity theorem of Birkhoff. It implies that the set of hypercyclic vectors of an operator is residual. Most results on common hypercyclicity are based on this result. Recently, Bonilla and Grosse-Erdmann have obtained an analogue of the theorem of Birkhoff for upper-frequent hypercyclicity. Based on this result we study common upper-frequent hypercyclicity. On the other hand, we obtain natural families of operators that do not possess common upper-frequently hypercyclic vectors.