U-Frequent hypercyclicity notions and related weighted densities

[en] We study dynamical notions lying between U-frequent hypercyclicity and reiterative hypercyclicity by investigating weighted upper densities between the unweighted upper density and the upper Banach density. While chaos implies reiterative hypercyclicity, we show that chaos does not imply U-frequent hypercyclicity with respect to a weighted upper density. Moreover, we show that if T is U-frequently hypercyclic (resp. reiteratively hypercyclic) then the n-fold product of T is still U-frequently hypercyclic (resp. reiteratively hypercyclic) and that this implication is also satisfied for each of the considered U-frequent hypercyclicity notions.

Disciplines :

Mathematics

Author, co-author :

Ernst, Romuald

Esser, Céline ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Menet, Quentin

Language :

English

Title :

U-Frequent hypercyclicity notions and related weighted densities

Publication date :

2021

Journal title :

Israel Journal of Mathematics

ISSN :

0021-2172

eISSN :

1565-8511

Publisher :

Springer, Israel

Volume :

241

Pages :

817-848

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 17 July 2019

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Bibliography

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