Dense Lineable Criterion for Linear Dynamics
Functional Analysis
2025-02-06 v1 Dynamical Systems
Abstract
We study Li-Yorke chaos for sequences of continuous linear operators from an -space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos. We show that in every infinite-dimensional separable complex Banach space, there exists a sequence of operators with a dense set of irregular vectors but without a dense irregular manifold, and we exhibit a recurrent operator whose set of recurrent vectors is not dense-lineable. This resolves in the negative a question posed by Grivaux et al.
Cite
@article{arxiv.2502.03352,
title = {Dense Lineable Criterion for Linear Dynamics},
author = {Alexander Arbieto and Manuel Saavedra},
journal= {arXiv preprint arXiv:2502.03352},
year = {2025}
}