Journal articles
CHAOS AND FREQUENT HYPERCYCLICITY FOR WEIGHTED SHIFTS
Abstract : Bayart and Ruzsa [Ergodic Theory Dynam. Systems 35 (2015)] have recently shown that every frequently hypercyclic weighted shift on p is chaotic. This contrasts with an earlier result of Bayart and Grivaux [Trans. Amer. Math. Soc. 358 (2006)] who constructed a non-chaotic frequently hypercyclic weighted shift on c 0. We first generalize the Bayart-Ruzsa theorem to all Banach sequence spaces in which the unit sequences are a boundedly complete unconditional basis. We then study the relationship between frequent hypercyclicity and chaos for weighted shifts on Fréchet sequence spaces, in particular on Köthe sequence spaces, and then on the special class of power series spaces. We obtain, rather curiously, that every frequently hypercyclic weighted shift on H(D) is chaotic, while H(C) admits a non-chaotic frequently hypercyclic weighted shift.
https://hal-amu.archives-ouvertes.fr/hal-03466290
Contributor : Stéphane Charpentier Connect in order to contact the contributor
Submitted on : Saturday, December 4, 2021 - 11:49:36 PM
Last modification on : Tuesday, January 4, 2022 - 5:53:30 AM
Contributor : Stéphane Charpentier Connect in order to contact the contributor
Submitted on : Saturday, December 4, 2021 - 11:49:36 PM
Last modification on : Tuesday, January 4, 2022 - 5:53:30 AM
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