Difference sets and frequently hypercyclic weighted shifts

Frédéric Bayart, Imre Z. Ruzsa

Research output: Contribution to journalArticle

40 Citations (Scopus)


We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on ℓp (ℤ), p ≥ 1. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is U-frequently hypercyclic but not frequently hypercyclic, and that there exists an operator which is frequently hypercyclic but not distributionally chaotic. These (surprising) counterexamples are given by weighted shifts on c0. The construction of these shifts lies on the construction of sets of positive integers whose difference sets have very specific properties.

Original languageEnglish
Pages (from-to)691-709
Number of pages19
JournalErgodic Theory and Dynamical Systems
Issue number3
Publication statusPublished - Aug 28 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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