Hereditarily frequently hypercyclic operators and disjoint frequent hypercyclicity
F Bayart, S Grivaux, E Matheron, Q Menet - arXiv preprint arXiv …, 2024 - arxiv.org
We introduce and study the notion of hereditary frequent hypercyclicity, which is a
reinforcement of the well known concept of frequent hypercyclicity. This notion is useful for …
reinforcement of the well known concept of frequent hypercyclicity. This notion is useful for …
Disjoint frequent hypercyclicity of composition operators
F Bayart - Advances in Mathematics, 2023 - Elsevier
We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We
apply this criterion to composition operators acting on H (D) or on the Hardy space H 2 (D) …
apply this criterion to composition operators acting on H (D) or on the Hardy space H 2 (D) …
Extending families of disjoint hypercyclic operators
In the present note, we solve two open questions posed by Salas in [33] about disjoint
hypercyclic operators. First, we show that given any family T 1,…, TN of disjoint hypercyclic …
hypercyclic operators. First, we show that given any family T 1,…, TN of disjoint hypercyclic …
Frequently recurrent backward shifts
R Cardeccia, S Muro - arXiv preprint arXiv:2407.11799, 2024 - arxiv.org
We study frequently recurrent unilateral and bilateral backward shift operators on Fr\'echet
sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent …
sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent …
On disjoint dynamical properties and Lipschitz-free spaces
The notion of disjoint\(\mathcal {A}\)-transitivity for a Furstenberg family\(\mathcal {A}\) is
introduced with the aim to generalize properties derived from disjoint hypercyclic operators …
introduced with the aim to generalize properties derived from disjoint hypercyclic operators …
Dynamics of weighted shifts on -sums and -sums
Q Menet, D Papathanasiou - arXiv preprint arXiv:2408.11153, 2024 - arxiv.org
We investigate a generalization of weighted shifts where each weight $ w_k $ is replaced by
an operator $ T_k $ going from a Banach space $ X_k $ to another one $ X_ {k-1} $. We …
an operator $ T_k $ going from a Banach space $ X_k $ to another one $ X_ {k-1} $. We …
A note on disjoint hypercyclicity for invertible bilateral pseudo-shifts on
SU Ri, HH Ju, JM Kim - arXiv preprint arXiv:2412.19115, 2024 - arxiv.org
We first give a note on disjoint hypercyclicity for invertible bilateral pseudo-shifts on
$\ell^{p}(\mathbb {Z}) $, $1\leq p<\infty $. It is already known that if a tuple of bilateral …
$\ell^{p}(\mathbb {Z}) $, $1\leq p<\infty $. It is already known that if a tuple of bilateral …
Mini-Workshop: New Horizons in Linear Dynamics, Universality, and the Invariant Subspace Problem
S Grivaux, K Grosse-Erdmann, É Matheron… - Oberwolfach Reports, 2024 - ems.press
Abstract The mini-workshop New Horizons in Linear Dynamics, Universality, and the
Invariant Subspace Problem discussed recent advances in the study of dynamical properties …
Invariant Subspace Problem discussed recent advances in the study of dynamical properties …