English

The Exact $\varepsilon$-Hypercyclicity Threshold

Dynamical Systems 2025-10-22 v4

Abstract

In this paper we give an affirmative answer to the problem proposed by Bayart in [J. Math. Anal. Appl. \textbf{529} (2024), 127278]: given ε(0,1)\varepsilon\in(0,1), there exists an operator which is δ\delta-hypercyclic if and only if δ[ε,1)\delta\in[\varepsilon,1)?

Cite

@article{arxiv.2509.09406,
  title  = {The Exact $\varepsilon$-Hypercyclicity Threshold},
  author = {Geivison Ribeiro},
  journal= {arXiv preprint arXiv:2509.09406},
  year   = {2025}
}

Comments

12 pages

R2 v1 2026-07-01T05:31:57.048Z